Sorry if it isn't as accurate as you hoped. I tried to find the song that Rhaegar sang but it doesn't mention it on the information about the tourney. I hope you all enjoy :)
*
The Hall was bustling with hundreds of people, talking, dancing, singing bawdy songs and enjoying the feast. Benjen crashed into Lyanna, setting her crown of winter roses askew.
“It was his fault!” Benjen exclaimed, gesturing to Brandon. For a moment, Lyanna forgot that she was a Lady, and shoved Benjen into Brandon, sending his chalice flying. She heard laughter and grumbles, mostly from Ned, who she hadn’t realised was between the two boys.
Although she knew it wasn’t proper to like one of her siblings more than the others, Ned was certainly her favourite. He could be overly serious at times, but he knew what to say and when to say it, and treated Lyanna like the woman she was. Everybody had a tendency to treat her like a child. A very beautiful child.
“What was that for?” yelped her brother, trying to polish his armour with a dinner cloth. Ned had already wiped his face down, and suddenly she felt truly guilty. People continued laughing, and as soon as Ned started laughing, she laughed too. She didn’t much care for her other brother’s feelings when she did things like this. In fact, she took pleasure from seeing their aggravated expressions. But when Ned was unhappy, she was unhappy.
Once the laughing died down, the champion of the tourney, Rhaegar Targaryen, rose from his seat at the feasting table.
“Is it not time for a song?” said Rhaegar, in his clear, mellow voice. Almost every person in the hall suggested a song for him to sing, but he silenced them with one gesture of his hand. He started to sing a sweet melody that Lyanna did not recognise. But she didn’t need to. His deep lilac eyes met her own grey ones and sang a song only for her. She fingered the crown of winter roses on her head.
Rhaegar had ridden up to her, his silver hair flowing behind him, and gently passed her the crown, naming her the Queen of Love and Beauty. Oh, the faces of them all. Bewildered expressions flooded the crowds. Though Ned, she had realised, had a stern face. She could not read his exact emotion though she knew he was not pleased. Yet she would never forget that moment. The moment she realised that she did not want to marry Robert Baratheon.
The song was over, and she realized that tears had seeped onto her cheeks. They were not intended, and all she could do was hope no one had seen. She gripped her sleeves and roughly wiped away her embarrassment. But it was too late.
“Crying are we? Look at the little baby crying!!” Benjen seemed overjoyed, practically bouncing up and down in his seat.
“Shut up!” she shouted. The first thing she reached for was her cup of wine. Soon enough it was plastering Benjen's hair to his forehead, stinging his eyes, dripping off the end of his beaky nose. This time Ned laughed as soon as it happened, and if Ned was laughing, then Brandon was roaring. The laughing infected the rest of the feasters. Lyanna’s stormy eyes scanned the room, the scrunched faces, the people falling from the table… And Rhaegar. He wasn’t laughing; he was just staring at her and smiling.
Without thinking twice, she blew him a kiss.
*
It's not very long, I know. Any recommendations for couples?
There will be more Lyanna and Rhaegar, I'll do parts.