I've heard two stories: Lithuanian liked Poland and was happy to join; and Lithuania didn't really want to join together but Poland's army was too strong to resist.
I just want some clarity on the information!
Well, the Commonwealth idea was planned quite a long time ago. There were some Lithuanians who thought "Hey, what a great idea" and of course there were those who didn't like it. Lithuania was forced to join the Commonwealth. Before the union of Lublin(4 months before it, on March 1st), the King of Poland and Grand Duke of Lithuania, Sigismund II Augusts, gave around half of the territory of Grand Duchy of Lithuania to the Kingdom of Poland. The territories included mostly Ukraine and some land near the border of the 2 countries. So a lot of Lithuanian nobles were angry about that, since the Grand Duke couldn't do it without the agreement of the council of nobles, but he did. Eventually, the nobles of both Poland and Lithuania signed the treaty, but there was resistance from the Lithuanian side. The leader of the Lithuanian delegation with most of the delegation, Mikalojus Radvila the brown(for some reason called the Red in the English wikipedia at least, tough that translation is wrong) left the meeting of both sides on March 1st and didn't participate in the eventual signing of the union, as did other nobles as a sign of protest. The Polish side also had some unreasonable demands, from the Lithuanian point of view. For example, they wanted to incorporate Lithuania to Poland, but that didn't work out for them. The Lithuanian nobles also felt threatened, because there were a lot more of Polish nobles and their legal status would be equal, which was not the best deal for the Lithuanians, being outnumbered. So to answer directly: No, Lithuanians didn't really want to join the union. There was no threat of a Polish army, threat of Muscovy more like. But what Lithuanians mostly did was protest the whole idea, because they didn't have much choice to it. There were no rebellions or any sort of these things immediately after the Commonwealth was formed.