Sorry this has taken me so long to get around to! I’ve been sick and working over time ‘cause other people are sick too :/ but thank you so much for your question :)
I’m not really sure it’s a one or the other kind of question. First of all, the Lannisters most likely always hated Elia in the first place. They would have to have been biased (particularly Cersei) because of the events surrounding Joanna’s death, Tywin’s subsequent refusal to marry either of his children to the Martells, his comments about Cersei being meant for Rhaegar, Rhaegar subsequently marrying Elia and then Cersei getting stuck with Robert. If I were Cersei I’d be pretty annoyed with everything Elia too, especially when we consider how bitter she still is over anything even mildly associated with her mother’s death (and rightfully so, I don’t blame her). Many people have been quoted as observing Rhaegar and Elia as having a happy marriage and I really, truly believe they did. It probably wasn’ perfect and they were probably closer to very good friends than passionate lovers, but I don’t think he was unhappy with Elia as a person. I think he was unhappy with their situation. Her health and the fact that they couldn’t have more children and more importantly, the stress of being around his father so much (who lets not forget was batshit crazy and probably as much of a dick at home as he was on the throne) added to the stress of everything expected of Rhaegar in his role as crown prince. I feel like it’s often understated, just how stressful that sort of position is for people (which is much the reason I fell in love with Robb), it sort of gets lost in this fantasy idea princes and princesses and ruling nobility have the easy, fun life. And in many ways they certainly have more comfortable lives, but the responsibilities and expectations are so much higher that it can be extremely stressful when the people in those positions take their roles seriously. I feel like Rhaegar never got time to really figure out who he was or what he wanted, he was just sort of forced to make the best of what was constantly asked of him. In Lyanna I think he sees an escape. This wild, funny, untamable, strong-willed girl who he can sort of take a backseat with while she takes the reigns, which has to be all sorts of new and relaxing for someone who’s always been asked to and expected to lead. Lyanna, also, is so far removed from the capital I think that has to play into it too. I certainly see them as the more passionate lovers than friends, but had they survived post war I really can’t fathom how that relationship would have actually worked long-term. I think I ship them a tiny bit more than I ship Rhaegar and Elia but…-shrug- it’s just a very complex situation. Which is why I love this series ;)