English = not first language.
1) Lisa Cuddy sucks at relationships.
She dated men from the internet, (and we all know that she likes sex so I don't think that she had long-term plans for the most of them) ruined every relationship she ever had, gave up trying to have normal family and focused on the baby. So she admitted to herself that she doesn't need love from a boyfriend or husband. And then Lucas came - and it turns out that she can be in something that actually works out. Even it may look silly - loser-like funny PI and kickass dean of medicine, that obviously something that works. Almost half of the season and still counting.
2) He can stand her.
Like Wilson said, Cuddy is a little crazy, and she needs someone to freak out around without feeling weird about it. Lucas accepts that she has weird relationship with House and Wilson that she don't want to give up and has full trust in her. He understands her guilty complex and the fact that House is her soft spot.
3) She's ready to fight for their relationship
(Ignorance is Bliss) even if it takes hurting House at some point. That means it's important for her.
4) She glows.
You can not agree with that, because it's very personal opinion. All season 5, when Cuddy had something to House, she was a little... Not herself. Because of her feelings she got totally dominated and became weak and I didn't like that at all. I liked her kickassness and the fact that she used to be mean sometimes (or maybe even more often) and that came back in season 6.
5) They are a family.
Cuddy has Rachel so she obviously need man able to handle the role of Rachel's dad. Lucas fits, and in this point I'm not trying to say, that no one else could, but the fact is that for sure he's close with her daughter. It takes a lot to bring someone new to the family, especially when you have a kid - so if Cuddy decided to do that, it obviously means something.
6) Lucas cares for her.
(Moving the chains) He's worried about her stuff even more than she is, and she's okay with that.
7) Photo below :)