In the UK, it seems to be similar to the States. If I see the name 'Lee' I presume it's a man.
It can also be a girl's name with that spelling, but for a girl it's more likely to be spelt Leigh these days.
Some parents also give girls the name Lea, or even Leah, and pronounce it 'Lee', which is very confusing. 'Leah' is a different name - it's a biblical name pronounced "lee-a" or "lay-a".