I think "Despite Lisa's parents' wish for her to possess a stable life, she dreamed of living more adventurously." would be the most natural way to construct that sentence. Unlike and despite have almost the same meaning, but unlike is more commonly used to show a difference between two things, for example "Unlike Lisa's parents, she likes to live adventurously." or "Lisa, unlike her parents, likes to live adventurously." This draws attention to the fact that Lisa likes to live adventurously, but her parents don't. Despite is used when something goes against someone's wishes, for example "Lisa likes to live adventurously, despite her parents' wishes." or the example at the start of the post. Both despite and unlike are common in formal and informal writing. I haven't really seen anyone use different in that way. Different is more used as "Lisa wants to be different." , "Lisa is different from her parents." or "Lisa and her parents think differently." I think "differing from" is also a correct way of saying "different", but I'm not too sure. If it is, it isn't used very often. Hope this helped!