After I defeated the Lion (9+ cows to spawn), no new set of goals appeared for me. The Horse still spawns Purple Glimmer Troll. I'm going to try the Dead Tree next.
Edit: They added Daily Goals. Dead Tree spawns Blue Dire Boar.
Edit: According to the first page, the first and only goal requirement was just to introduce the Lion. I hope the game makes it more clear in the future so that players don't expect more and think the game is bugging out like the previous event.