Back home Lara is a celebrity super-hero. Not a particularly active super-hero, but because she looks good doing it she's become a media favorite. With that comes the usual social life problems, like trying to identify who really cares about her rather than using her, etc. She spends most of her time at home in a small circle of friends, and really doesn't get out much because it's difficult to do so without photographers chasing her everywhere.

The Lair Mansion is one of her escapes. She can visit there in relative obscurity all she wants; but she still misses home and her friends there, which is why she doesn't stay in the Parodyverse all the time.

As for where this story fits into Hatty's love life...I guess Lara's point would be that it doesn't.

Any questions?