Hesitation to use "girlfriend" in reference to old people

Solution 1:

As ShreevatsaR said, it’s perfectly straightforward: for many speakers girl still means (or at least strongly connotes) a female child or at most a young woman, and for those speakers a woman who is likely to be dating a man in his late 60s simply isn’t a girl. And if she isn’t (in their terms) a girl, it’s entirely understandable that she can’t be a girlfriend, either. No further explanation seems necessary.

That said, there is considerable variation, and a fair number of speakers would have no hesitation in calling her his girlfriend. For example, even at 63 I’d still be comfortable calling a woman my girlfriend, unless of course she herself objected to the term, and I’d have no objection to being called her boyfriend. For me (and many others) the meaning of these terms is no longer strictly compositional.

I see nothing comical about lady friend; at worst it has a slightly old-fashioned feel, and it’s an obvious choice for someone who finds girlfriend inappropriate on grounds of age. For those who find it too much of a period piece, there are always the very modern significant other and the neutral partner.