Christian Heresies like the Cathar and Lollards were all crushed under Catholicism and brought back into the fold. Were there any conflicts like this against Orthodoxy?

Unlike the Western church, the Orthodox church did not have one central prelate (the Pope) to direct church policy. Partly this is because unlike in the West, where Rome is the only "Apostolic See" (founded by St. Peter) and thus the Bishop of Rome is the only "heir" of an apostle, in the Eastern church there were a number of Apostolic Sees, including Antioch, Constantinople, Alexandria, and Jerusalem. So no one Bishop in the East had the primacy that the Bishops of Rome could and eventually would claim.

This meant that Eastern Churches tended to be more localized in practices, holidays, and to some extent, theology than the Western Church, altho this of course varies throughout the history of both, which is thousands of years long.

A number of different teachings, orders, sects, and heresies arose in Eastern Christianity, and there was less ability for any one Bishop or Church Leader to denounce them as explicitly heretical. If they were denounced, it tended to be in concert with secular authorities, who held more sway over the Eastern church as a rule than the Western, but again, that varies greatly depending on what time period you are discussing.

One example of an Orthodox heresy I'm familiar with: The Russian "Old Believers", which interestingly enough were actually a reaction against reformations in the church. In the seventeenth century, the Patriarch of Moscow, with the support of the Tsar, implemented some liturgical reforms intended to "return" Russian Orthodox practices to those practiced by Greek churches. One of these reforms was to have blessing performed with three fingers, symbolizing the trinity, rather than two as had been done previously.

In Orthodoxy at this time, the rituals were a vital part of connecting the Church to god. The Church traced their lineages directly back to the apostles, and thus their practices had been devised by those who knew the Christ personally. If those practices had altered or decayed, the Church's connection spiritual with god would similarly decay, which is of course a theological crisis. Unfortunately, many Old Believers clung to the old practices as the "True" ones, and rejected the new practices as the corruption. In challenging the authority of the Patriarch, the Old Believers were challenging the power and order of the Russian state, and were thus viciously prosecuted by the Tsar. Many high-ranking Old Believers were executed (in one case they barricaded themselves inside their church and set it on fire themselves. Their spiritual crisis was such that they would rather burn to death and join their god than alter their liturgical practices and thus be cut off from him forever.) Many others were exiled to Siberia, and can still be found there today.

Old Believers are extremely rare these days, in part because they had the almost unique position of being anathema to both the Tsarist AND the Soviet regimes, albeit for differing reasons. So that' s one incidence in one country, there are plenty of others.

TL;DR: Yes, of course there were. We're talking people and religion here, of course they came up with ways to kill each other over it.