Parents: How would you feel about this?

Is this before or after he apologized to her? Does she even want to reconcile with him? If he approached me before settling this with her, I would think it was manipulative and tell my daughter as much. It's disrespectful not to prioritize her when she is the one he wronged. I would think he is just looking for a way around her boundaries. Otherwise, if they had already reconciled and he is just trying to make peace with the family, I would probably accept the apology and appreciate that he made the effort. That's assuming they didn't break up because he was abusive or toxic. Abusers don't get second chances, asking for one at all is proof he isn't truly remorseful. 

I would be deferring to the judgement of my daughter on whether or not she wants him in her life.

I wouldn't think he was lame .. infact I would feel for him, unrequited love hurts. 

But, I'd also speak with him about relationships in general - every relationship has hurdles and usually challenges present themselves so that we can gain knowledge and understanding of ourselves and what we are looking for. 

They help us grow. 

I'd make it clear that my daughter is not available & that she has moved on and wish him well. I'd also suggest that some counseling might help... Oh...  and the mother bear would also make it very clear that it would be best for him if from now on, he respected my daughter's right to privacy & keep his distance.