My sister-in-law's birthday is in mid-March, and, consequently, always during Lent.  She has struggled with how to observe her birthday (if at all) so as not to disrupt the Lenten observance.  She's not a child anymore, so she's not worried about having a party or anything like that, but, like most people I think, she would like to have a nice dinner and perhaps a cake on her birthday.  In the past, some years she's totally ignored her birthday, other times she waiting until after Easter to acknowledge it, sometimes she celebrated it on a Sunday in Lent.

It's a milestone birthday for her this year, and my husband wants to throw her a party, if not on her birthday than on the Sunday following it.  What do you think is appropriate?  Is gift-giving, a family get-together, a fancy dinner, and cake compatible with Lent, even if its for a birthday?

We always celebrate on the Sunday after - or before, depending on which day of the week the birthday actually falls on.

Essentially, this. This is how we do things in my family in general - not only because my own mother's birthday can fall during Lent, but because it's easier overall.