oh yea, it can be hard! from everything you've posted, though, it appears George doesn't HATE Gigi, which is a very good sign!
plus George is a senior doggie --- having puppies around, esp. a Lab puppy :wacko: :blink: :wacko: , can really wear those oldsters out. it's one reason i haven't even considered a young doggie even though i want one and even though one was even dropped in my lap a month or so ago --- some kind of coonhound mix, a lovely girl who moved onto my front porch. but a completely insane puppy! personality-wise, Lady could handle it. but Lady is pretty physically frail, so i couldn't.
George isn't frail, though, so that's another point in your favor.
so ... basically they get along and George is hardy enough to handle Gigi ... to a point!
my prescription thus far is therefore --- ? --- :
1. give it time;
2. figure out someway for Gigi to work off some of that crazy lab energy so she isn't driving George absolutely bonkers and doesn't wear him out, thereby making him grumpy.
also, Gigi might be either a dominant dog or didn't have a chance to acquire proper doggie manners. Lady is submissive but from what i can tell, didn't get the chance to acquire proper doggie manners. she drove Biscuit absolutely insane because of this. it took her some time and she still falls back into old patterns (she's an old girl, remember), but she did learn not to leap into the middle of everything and to mind her manners!!!
so maybe consider puppy classes for the lab --- or otherwise some way for her to begin acquiring better manners, if she's pushing George out of the way or vying for attention when you and George are having a little alone time. remember, she might be needy, but she's now a member of your household and she needs to abide by the rules. she and George and YOU will be happier once she figures those rules out.