As of right now there are no new missions in LT, however they are a planned feature.
"They may request more land, or they may request something entirely different. For instance, the nobles may give you a mission to increase serfdom, lower the influence of the bourgeoisie, or perhaps declare war on another country. The rewards from completing the mission would vary and would depend upon what the mission was and which social class had given it. They would of course have to have a certain amount of influence to even give you a mission, and the completion of a mission would always increase that group's loyalty. But missions won't be in the next update.''-Jnt.mullen