So a bunch of people are convinced that the dragon prince and the wolf maiden had this great lovd affair but I'm not sold.
Let's look at some facts - I believe that Lyanna was our mysterious knight that Rhaegar found but there's no indication that the two spent any personal time together between then and when Lyanna was crowned Queen of Love and Beauty. Cut to roughly a year later when Lyanna was "kidnapped". First she must have already been heading south since she ended up in Dorne before Brandon rode to Kings Landing from Riverrun. My guess she was supposed to be going to Storms End although Riverrun and the Vale are other choices. Now let's keep in mind the timeline - Lyanna was 16 when she died, 15 when the war began and 14 at the tourney of Harrenhall. So it seems possible that she was infatuated with Rhaegar and might have turned to him to escape her unhappy engagement. Maybe during that year she fell in love but it wasn't that way at first.
Now switching to the last dragon - most remember Rhaegar as a man who would have been a great king but I see something else - an obsession with the Prince that was Promised prophecy. From the House of the Undying vision, he was already looking to have another child, his third head, after Elia was advised not to get pregnant again. But why Lyanna? Well he already had a Rhaeyns and an Aegon so he needed a Visenya and who better to be the mother of the legendary warior woman than a girl who would secretly disguise herself as a knight? Also it would unite the blood of the dragon with the blood of the first men. Now Rhaegar would have had to have known that seemingly abducting the daughter of one great lord and the fiancee of another would cause a lot of problems but his obsession with the prophecy came first and it cost thousands their lives. Again, maybe he came to love he but that wasn't his original intent. Perhaps he didn't fully escape the Targaryen madness after all...