I really doubt it, Robert was notorious for messing around with lowborn girls but he would have had more respect for a highborn lady like Lyanna and he was betrothed to her anyway so he would have been able to wait, and not dishonor her because he seemingly liked her so much
But some say that he might not have even loved her really, he hardly actually knew her and he was just in love with the idea of her, she was his and another man stole her. She was just a girl he fancied at the time and tragically lost her, it's not like they had built up undying love for years like Ned and Catelyn did.