I think what David said, complimenting Lisa to to face when they were by the pool, and then bagging her behind her back when he was with the guys was pretty weak, and he owed her a better apology than the one he gave.
Two reasons: Firstly it is the right thing to do. Secondly because if he wants to stay in the game he needs to keep people onside. He needs to sharpen his diplomacy skills.
His apology did not come across as sincere and actually made the situation worse. Calling Lisa over to him as he did, combined with his body language (arms spread-out behind his head, communicates "I am smarter than you"), implied his own superior status. This would have aggravated Lisa even more. Moreover he didn't really apologize for what he said, but rather the way she felt, which suggested that it was her problem alone.
Rather I think he should have gone to her, offered a sincere apology, and accepted full responsibility. He should taken the words back and said he did not mean it at all, and been honest that he was just trying to bond with the guys, and that it was just a case of foot in mouth. That followed by a little self-deprecating humour might have fixed any ill feeling.
Instead David chose to console himself with having the boys on his side. But at the end of the day he's not really one of the boys. They only just begrudgingly accept him. Plus now he has made a real enemy in Lisa, and will have lost the respect of most of the girls.
David needs to lift his game quick smart or he will be one of the first to go.