Here's where I'm coming from: I think your theory has some merit, but I'm not convinced, because there is no evidence to support it. It's just a good idea. We'll go through evidence below.
You just said to me in your reply - Because earlier you were telling me that my theory doesn't make sense because "Lyanna wouldn't leave her engagement to Robert Baratheon", when (unless she left it by force) that is exactly what she did.
SHE DID LEAVE IT BY FORCE! THAT IS RIGHT IN THE BOOK!
This is a perfect example of what's wrong with your theory. The war started because Lyanna was kidnapped and raped. I can look that up and copy it from the books and show the pages numbers it's written on. That's evidence, it's book canon. However, your theory is claiming she ran away willingly, so you're saying the book is wrong. Am I supposed to listen to you instead of GRRM? If your theory is going to say that she wasn't kidnapped and went willingly and the book is wrong, then you have to prove that by showing us quotes and foreshadowing with page numbers to show us how you came to that conclusion. Saying "Everybody in the books said Rhaegar was super-dooper chill so he wouldn't rape her, so I think she ran away" is not evidence, because the book tells us he's super nice, but the book says he kidnapped and raped her too.
You're forming a theory, so you don't have to have proof for every opinion or everything you say, but there has to be enough proof to seem logical. Also, you can't assume that everyone remembers every quote about every character, like the conversation between Ned and Lyanna about Robert. Add the quote and show why you think she didn't want to marry him. Back up your shit. Read through theories here that have really high up-votes and see how they basically lead the reader through the entire thought process by showing them the quotes and foreshadowing. Go on you tube and look at Preston Jacobs video theories. He sites quote after quote after quote.
Your theory doesn't prove:
she left willingly and wasn't kidnapped
it was political
that she would betray her family
it wasn't about the PTWP
she knew about the super secret alliance
she didn't want to marry Robert
that she'd want to have a bastard
that she didn't want to marry Rhaegar