In all honesty, when Biff first met Lee, he thought she was a boy like everyone else did. When they had detention together, he was annoyed with 'him' until he realized that 'he' was definitely not a boy. He didn't know whether he wanted to laugh or ask why, but with how everyone else was fooled by this flimsy 'disguise' he had laughed.
She'd stared at him strangely, but had brushed it off and that was when he helped her with her little mission.
He didn't know how the other students were fooled by the clothes, but it might have had something to do with the fact Lee never really smiled all that much, and she was kind of cold.
When Lee had snuck out to the football team's try out, he was almost worried about whether or not Lee would be able to handle herself because she was a smaller than those guys. But she was fast, and that would make it harder to catch her he supposed. She'd made it back within only seconds of Barrage and after they'd been dismissed, he didn't know what made him put that blanket on her.
She looked worn out and tired, so he let her sleep. Her mother would have come and got her anyway.
After that, Lee had begun to look at him strangely, and she seemed to be thawing out 'cause she started to smile more. And then, there was that kiss. The one she had given him on the day of Brandy's party and had awkwardly seemed like she was asking him to go with her. She'd kissed him right on the lips, and with her face flushed and embarrassed, had fled the detention room.
He didn't try to go after her because he was in shock himself. He didn't even notice that Lee seemed to like him, so this had been a bit of a surprise. She'd probably awkward around him or try to act like nothing happened, so he'd do the same. When he found out she broke up the DoD, he'd gotten really angry that she could have done something so stupid and that kiss was the last thing on his mind.
But after the Battle of the Bands, he couldn't keep it to himself and threw her a bone that he hadn't found the kiss to be unenojoyable.
Though he really did think that it was going to be the only kiss between them because she liked him and he was starting to warm up to her despite trying to pretend nothing changed. So when she brought up the kiss, he relayed to her his thoughts on the matter and she had gotten frustrated with him.
They kept dancing around the subject from then on until she pulled him to the side at the docks of the field trip and had poured her heart out to him, and he had listened. The kiss was better than the first one because it was their 'real' kiss, and he was willing to try with her if she was with him. Well, she had to be willing after all they'd been through and she still liked him despite him being…him.
He liked Lee, he really did, and even though he wasn't quite comfortable with trying to push their relationship into the open, yet at least, if they could get through her mother trying to keep them apart, then maybe they really could get through anything.