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And if she insists on getting off, how would you "save face"
I lead her by the hand to a semiprivate place and get her off obviously.
All kidding a side I usually only let a girl sit on my lap in public when I'm at a house party. That way I have an excuse to tell her to get up whether I want another drink or just become too warm with her sitting there.
If she wants to get up or just gets up, who cares? I'm already talking to someone else anyway.
Lap sitting can be an attention seeking behavior or a sign of comfort. Rarely is it an outright expression of a sexual behavior (unless she's in a mounted position).
In the club/bar having her on your lap is going to increase your chances of getting LMR later.
As for girls moving closer to you it is usually a sign she wants you to talk to her. If you take the time and pay attention when you're out at the bar you'll start to notice women will come and stand right next to you when they are ordering when they could have went to a number of other places along the bar.
Often they will also unnecessarily thrust out their butts or arch their backs pushing their chests out. This is girl speak 101 for "notice me".