It's so easy to fall for her.
She is beautiful, dark brown hair blowing freely in the wind, so different from the complicated hairstyles of the south, stormy grey eyes staring into his defiantly. She is wild, she is untamed, she is free. She has a strong sense of honour, but she will not let anybody tell her what to do. She is the complete opposite of Elia, his beautiful, dutiful, quiet wife. Lyanna has to be heard, to be seen. She could never fade into the shadows like Elia does. Lyanna fights back, she yells at him, she refuses to back down. She is everything Rhaegar ever wanted.
And so he takes her with him. They run together, marry in front of a weirwood with only Arthur and Oswell as witnesses, elope to Dorne. He is sure that nobody will search them there, in Elia's home, and he is right. They spend blissfully happy months there, just the two of them and his two friends from the King's Guard, and Lyanna teaches him to forget about prophecies and live in the moment.
Their peace was shattered when Ser Gerold found him, but he hadn't told Lyanna that. Not when she was pregnant and already not feeling well. She had smiled at him when he left.
It was this smile Rhaegar thought of when he fell to the ground, defeated and dying.