The short answer is that Lenin was just as or almost as authoritarian as Stalin, it's really just a question of scale. The long answer follows.

• Both of these men ruled a nation with absolutely no political pluralism; neither sought to change that.
• Both of these men launched huge, organized, and far-reaching terror campaigns on their enemies and perceived enemies.
• Both of these men established and granted mostly unchecked authority to secret police organizations, and then empowered psychopaths to run said agencies.
• Both of these men purged the political ranks of their own party (to say nothing of their opposition) in order to consolidate their power or the power of an oligarchic faction at which they were the head.

The system of which both of these men sat atop was inherently authoritarian. There was never any secret about that. Just because Stalin's body count was higher and he proved to be the more effective mass murderer only makes him worse when considering the substantive result-- not when trying to compare their ideological or ethical culpability with respect to being an authoritarian. I guess that's kind of a value judgement though, so please take it with a grain of salt. Also, before going any further, it's probably best to define our terms since 'authoritarian' is one of those words that gets thrown around a lot without a clear understanding of what it actually means. I'm using Yale Sterling Professor Juan José Linz's definition of authoritarianism from Totalitarian and Authoritarian Regimes (2000) but there are plenty of earlier works by the same author and others which provide almost identical criteria:

Political systems with limited [...] political pluralism, without elaborate and guiding ideology, but with distinctive mentalities, without extensive nor intensive political mobilization, except at some points in their development, and in which a leader or occasionally a small group exercises power within formally ill-defined limits but actually quite predictable ones. [1]

So obviously, we need to factor in that Marxism-Leninism was an explicitly guiding ideology in the RSFSR and Soviet Union and therefore according to Professor Linz (and others like the late Richard Pipes), we would be better to classify these rulers as 'totalitarian,' but the rest of the mentioned criteria most certainly apply and I'm not here to try to correct your word choice. Despite taking the time to spell out what 'authoritarian' actually means, I think I understood what you meant when asking the question and any reasonable reader would too.

Okay, hairs split. Moving on. Lenin was in a position of supreme power over the Soviet Union as the Chairman of the Council of People's Commissars for just over a year (December 1922 to January 1924); the vast majority of that time he was almost completely incapacitated as he had suffered a series of debilitating strokes (May 1922, December 1922, March 1923). The second of these left him almost completely immobile and rendered him, for the most part, unable to speak coherently. The third left him bedridden. Before any of that though, Lenin was nominally in charge of the USSR's first incarnation-- the Russian Soviet Federative Socialist Republic (RSFSR)-- from November 1917, until the Soviet Union was formed 5 years later and he assumed leadership of that state.

First Secretary of the Communist Party Nikita Khrushchev, who succeeded Stalin (after a fashion) and changed the title of the de facto ruler of the Soviet Union to 'First Secretary' of the Communist Party (so as not to hold the same, tainted title as the recently deceased Stalin of 'General Secretary'), drew many distinctions between the two. Almost none of them stand up to honest historical inquiry but he did draw one important distinction: Lenin never killed a fellow communist (which should be more truthfully said, Lenin never persecuted a fellow Bolshevik communist who had enough clout to merit a following). His more famous persecutions (which were numerous and ruthless but go unmentioned in Khrushchev's so-called Secret Speech) were mostly limited to class enemies like Russian Orthodox priests and nuns, practicing Jews, Caucasus Muslims (less so than the other religions of the book though, because Lenin shrewdly used Islamic leaders to foment resistance to imperial rule in favor of the Bolsheviks), sympathizers to the defunct imperial regime (wealthy or otherwise), 'informers,' foreign diplomats and their employees, Menshevik oppositionists, and just about anyone else who could be framed in any way as a counterrevolutionary or reactionary element.

Lenin's functional number two, Lev Trotsky, addressed the state-sanctioned use of terror thus:

[T]error can be very efficient against a reactionary class which does not want to leave the scene of operations. Intimidation is a powerful weapon of policy, both internationally and internally. [...] The State terror of a revolutionary class can be condemned 'morally' only by a man who, as a principle, rejects (in words) every form of violence whatsoever-- consequently, every war and every rising. For this one has to be merely and simply a hypocritical Quaker. [2]

I don't know about you, but to equate individual executions perpetrated on a mass scale with collateral damage during wartime (which is of course no less tragic), smacks of something disingenuous. Namely, that at the very least, the former is far more personalized-- which I suppose Trotsky would argue just makes it more honorable. You can be the judge of that.

Anyway, this is the man, Lenin, who intellectually architected Vanguardism. The idea that an oligarchic group with the 'best interests' of the proletariat in mind needed to head the workers' state until the appropriate conditions for 'true' workers' control could be implemented. That is the exact authoritarianism that Stalin inherited and exercised upon Lenin's death. Stalin did take the singularity of that authoritarianism to new heights though, which is why at the outset of this answer I couched my statement with the caveat 'almost' as being potentially appropriate, based on whether or not you personally believe orchestrating the conditions for a madman to make near-limitless power indeed limitless merits condemnation.

From Khrushchev's On the Cult of Personality and Its Consequences (colloquially called the Secret Speech):

Being a militant Marxist-revolutionist, always unyielding in matters of principle, Lenin never imposed his views upon his co-workers by force. [3]

But who were the Mensheviks, Mr. Khrushchev? Instead of just shooting them in the back of the head as Stalin preferred to do with his well-known political opponents, Lenin rather saw that they were simply driven from Russia. Objectively more moral than Stalin? Sure. Less authoritarian? Not really. Even Isaac Deutscher, the Polish Marxist who was perhaps among the best biographers and apologists for the Bolsheviks, Lev Trotsky, and other similar figures from the period wrote the following in his 1965 essay The Mensheviks: Exile and Debasement:

[The Bolsheviks] took to persecuting the Mensheviks with a panicky brutality, which was, however, tempered by cautionary historical reminiscences, scruples and forebodings. Lenin did not wish to guillotine Russia’s Girondins. There was no great purge of the Mensheviks, no execution of their leaders. Martov, Dan, Abramovich, Nikolayevsky and other lesser lights were allowed, or rather encouraged, to leave Russia and establish their political centre abroad. [4]

Was this done out of mercy? I think the historical record, Deutscher's own writing, and the future actions of the Bolsheviks with respect to the remainder of the former imperial Romanov family show explicitly or, at the very least, implicitly otherwise. Lenin was an historically minded figure. He had studied the French Revolution immensely and he knew history would judge his actions one day with perfect certainty. Thus, just killing all of his political opponents as opposed to driving them from the country (where they could serve his ultimate ends of sowing world revolution, but not challenge his local grip on power in any meaningful way) was the worse of two choices.

Likewise, there is no document which shows that Lenin or anyone higher than the Chairman of the Ural Soviet (essentially a political nobody) ordered the execution of the Romanovs that fateful July morning. Does that mean he didn't have anything to do with it? It's still debated whether Lenin even knew about it. Many contemporaries involved in the events directly support both sides. It's a matter of historical debate to this day. For the sake of your question-- as the culpability of Lenin is quite important here-- let's say that Lenin did not order the murder of the Romanovs (which I personally don't believe to be true for a minute, by way of the testimony provided by Yakov Sverdlov to Lev Trotsky, noted in the latter's personal papers, that Lenin himself not only ordered the execution, but ordered that any evidence of his involvement be suppressed).