A few reasons.

First of these being that Lithuania was notably tolerant for other religions and cultures, and, in addition to that, was especially great at integrating conquered nations into their empire. Regions and principalities conquered by the Lithuanians were allowed to maintain their own customs and sets of laws, only with a Lithuanian duke in charge. In many cases, lands conquered by the Lithuanians even continued to pay tribute to the Mongols, and more diligently than the Ruthenian princes before them. Conversion of the Lithuanian nobles ruling over Christian territory was also encouraged - this was the case with many sons of Gediminas and later Algirdas, such as Teodoras of Kiev or Andrew of Polotsk.

What this equated to was that Lithuania, despite officially being pagan, was treated as a Christian one in many situations - for example, Algirdas verbally fought with the Prince of Moscow and later the Byzantine Emperor over the control of the Metropolitan of Rus' (despite being a Lithuanian pagan ruler!), and the House of Gediminas often married into Christian royal families, the most famous example being Prince Casimir of Poland (later Casimir III) marrying a Lithuanian princess.

Second... Lithuania really didn't. In fact, it's almost a miracle, and not a good one, that Lithuania remained pagan as long as it did - the stubbornness of the Lithuanian rulers means that the 14th century was one of the bloodiest periods of Lithuanian history, sometimes dubbed as a "hundred years' war". By the time the 15th century arrived, according to modern estimates, 400 thousand Lithuanians lived in the Grand Duchy and 300 thousand lived in the Teutonic Order as slaves or descendents of former slaves (they later formed the nucleus of the Prussian Lithuanians) - that's how much of a toll the constant conflict with the Christians left on the Lithuanian nation.

Lithuanian luck manifested in a number of ways - Lithuanian efficiency in adapting Western technology (according to chronicles, only a year passed from the first Teutonic use of the cannon against Lithuanians to the first Lithuanian use of the cannon against the Russians), surprisingly easy Lithuanian expansion into the east (Though it struggled at some points), Gediminas's successful trickery of the West by promising to convert and using the Papacy's mandated peace to recover and expand east, so on and so forth.

Main source: A. Dubonis and others, "History of Lithuania", III tome

Lithuania is (in various sources available in English) considered only to have coalesced as a state in the early 13th century, being previously an area of various smaller tribal cultures. Over a period of approximately two hundred years, it expanded rapidly (map) and was anything but a static entity.

The Grand Duchy emerged into written history in 1219, in a treaty with Galicia–Volhynia. Writing can be seen as a development which went hand-in-hand with Christianity, and the question may imply the difficulty of maintaining a state without writing.

This also, obviously, spells difficulties for historians. In 1989, Stephen Rowell, a Cambridge historian who later emigrated to Lithuania, wrote that “A scholar interested in the history of an English county in the 14th century may find himself confronted with more primary sources than a historian of the Grand Duchy of Lithuania involved in studying the same period.” There is a limited amount of material to go on even for those who know all the relevant languages, and significantly less in English.

But the country's official paganism can actually be seen as advantageous for a time, in making it possible to play off Eastern Orthodox and Western Catholic powers without being clearly committed to one world or the other (Frost, 2015). By 1377, the organisation of the pagan grand duchy was, however, hitting its limits.

Frost (2015) highlights the geopolitical advantage held by the Lithuanian heartland in the 13th century. It was especially remote: "travelling fifteen leagues from Dyneburg to Vilnius in 1414, the diplomat Ghillebert de Lannoy entered a vast forest in which he travelled for forty-eight hours without seeing a trace of habitation". This forest can be seen as instrumental in protecting the core of Lithuanian power from both the Teutonic Knights (who were encroaching on Livonia, what is now Estonia, and the coastal areas) - and from the Mongols who were sweeping across other parts of Eastern Europe. Mongol troops were unsuited to warfare in large dense forests, and moved on to more fruitful areas.

Lithuanians also took advantage of the damage done by Mongols in adjacent territories. Frost takes the view that the Lithuanian Grand Dukes were a bulwark against Mongol domination of the region, especially as the Ruriks of Muscovy were weakened at this time. Baronas & Rowell (2015, p.158) also state (elaborating on the point made by u/Augenis) that "the tribute from much of the Ukrainian lands was paid to the Tatars much like before and the sovereign rights of the Golden Horde were not put into doubt until the late fourteenth century."

Initial expansion in the 13th century often took the form of raids into neighbouring states. Mindaugas - Grand Duke from c.1236-c.1251 and King to 1263 - converted for a time to Christianity. Baptised in 1251 under the sponsorship of the Teutonic Order, he took delivery two years later of a crown from Pope Innocent IV. Formal recognition as a king was a privilege granted by Christendom only to other Christian rulers - one of the benefits OP is no doubt referring to. However, the conversion proved politically tricky at home. Historians agree that the Teutonic Knights were perceived as a major territorial threat, and that this was a major reason the boyars opposed Mindaugas' Christianity. He returned to paganism in 1261, but was nevertheless assassinated, along with his sons, two years later.

Baronas and Rowell (2015) interpret the political role of Lithuania's pagan religion as politically useful rather than subject of devout religiosity. In this, they align with recent understandings of other European paganisms (which will be familiar to those who've read a few AskHistorians answers about conversions in Western and Northern Europe). It is also a break from a number of other, earlier histories of Lithuania:

Princely blood and patrimonial rights were what really counted. It follows that all this stark opposition of Christian versus pagan is a concoction of Teutonic (and other Christian medieval) chroniclers, an opposition which, prior to being critically evaluated, found its way into modern historiography thus giving rise to the image of the most obdurate Lithuanian pagans, among whom Zemaitijans [Samogitians] had no match. (p.334-335)

Even Frost, also published 2015 - but based in the UK - who does not place great emphasis on pagan devoutness in the manner of some earlier secondary sources, suggests that the pagan religion was in itself a motivation for boyars at any time when it was under threat.

The next significant waves of expansion took place under Vytenis (1295-1316) and Gediminas (1316-1341). Whilst there were some military conquests, this Gediminid dynasty also produced a great many offspring and created future rights to territory by strategic marriage alliances. These youngsters who were sent off to marry also had to convert in order to do so, more to Orthodox Christianity, though a few also headed westwards. (Lending soldiers to Mazowia and Poland at strategic junctures was another means by which Lithuania made alliances, before the raids on Poland of the 1340s-1370s. Newly acquired territory could also be given to other children and relatives. These networks of related rulers under the charismatic leadership of the Grand Dukes were, in the opinion of Frost, one of the most important means by which the greater Lithuanian state functioned, despite its relative lack of Western-style administrative structures.

The territory was not devoid of writing and administration: in the annexed Ruthenian territories, the Ruthenian language remained the language of writing and state structures; its adoption by the Lithuanians enabled the Gediminid state to consolidate and expand - and the Ruthenians to integrate.

Another use of writing is also seen in the letters of Gediminas to the Pope in the period 1322-24. Surprisingly wily choice of phrasing is used on a key point, considering these letters are thought to have been dictated by Gediminas and rendered to Latin by a monk. (Christians were welcome to live in the Grand Duchy, so long as they did not proselytise excessively or criticise the pagan faith.) For political leverage against the Teutonic Knights, he implied strongly to the Pope that he was thinking of converting to Christianity. Papal envoys made their way to the court at Vilnius under the assumption he would convert. He could argue with them that he had not said that, and had been mistranslated by the scribe, but in fact the Latin, (‘fidem recipere’) was cleverly ambiguous too.

By 1377, the Grand Duchy had expanded nearly to the Crimea, and there was little easily-conquered territory which could be given to further offspring, the state became precarious after the death that year of Algirdas. Muscovy was in the ascendant again and the Polish-Hungarian alliance led by Louis of Anjou was gaining territory to the west. More of the Gediminid clan than not were Orthodox by this time, and regardless, there were simply so many of them that the state was at risk of the fragmentation that had affected Slavic states with similar systems of inheritance.

It was in this post-1377 period that Algirdas' son Jogaila, the future Władysław II Jagiełło of Poland, was again engaged in the game of playing off Catholic West against Orthodox East, for the purpose of a marriage alliance that would save his power in a tumultuous period marked by conflict with his uncle Kęstutis. Marriage with a Muscovite princess and conversion to Orthodox religion, as mentioned in a peace treaty of 1383-4, risked making Lithuania a vassal state, but he manoeuvred to secure the alliance with Jadwiga of Poland, which would appease the Teutonic Knights and give his country greater autonomy, as well as alliance with the powerful Western Catholic church.

References

Darius Baronas & S.C. Rowell, The Conversion of Lithuania: From Pagan Barbarians to Late Medieval Christians (Vilnius: Institute of Lithuanian Literature & Folklore, 2015)

Robert Frost, The Oxford History of Poland-Lithuania Volume 1: The making of the Polish-Lithuanian Union 1385-1569 (Oxford University Press, 2015) (Chapter 2, pp.18-35)

S. C. Rowell, 'Lithuania and the West 1337-41 - A Question of Sources', Journal of Baltic Studies 20 (1989), pp. 303-326.