Were Lyanna and Rhaegar in love?
The general consensus is that Rhaegar captured Lyanna after growing infatuated with her at the Tourney of Harrenhaal, a celebratory festival that brought together many noble families from across the Seven Kingdoms. Rhaegar was married to Elia Martell -- sister of Oberyn -- at the time, and had two children, Rhaenys and Aegon, but this didn't stop his pursuit.
But while the Rhaegar-Lyanna relationship looked like an abduction, there's reason to believe that she went with him willingly, and that they were deeply in love. For starters, Rhaegar was admired by those in his orbit, including Barristan Selmy, who served the Targaryens. "Rhaegar never liked killing – he loved singing," Selmy tells Daenerys of her brother. Rhaegar's gentle nature is relayed by many, and in the books even Ned doesn't think of him as dangerous. There's even more evidence if you go looking, but long story short, it's pretty likely that Rhaegar and Lyanna's love was mutual.
Were Lyanna and Rhaegar married?
Unclear. The Targaryens were known to practice polygamy, and some fans even speculate that Rhaegar was able to annul his marriage to Elia and secretly wed Lyanna. There's no proof of any of this, but it does seem likely, if only to legitimize Jon's birth.
But that means…
Yup. Rhaegar's eldest children were murdered in Robert's Rebellion, so if Lyanna and Rhaegar were indeed married, that makes Jon Snow the rightful heir to the Iron Throne – above Daenerys, who would be his aunt.
This is a big deal. Not only does it complicate Dany's conquest of Westeros, but it also lends a poignancy to Jon's resurrection, making it more of a rebirth – Jon Snow is dead, but Jon Targaryen lives. Martin's series is called A Song of Ice and Fire, and if Jon is half Stark (ice) and half Targaryen (fire), it's likely that he's the ultimate hero of the story – the one who will unite the kingdoms, either by serving as king or by destroying the White Walkers. Perhaps he'll even ride a dragon.