someone asked me to re-install office XP, but she has lost the license key she got when she bought her computer. Is there any (legal) way to get a new license key ?

P.s. don't even think about mentioning OpenOffice

If this Office XP was purchased (not installed as OEM) and registered with Microsoft, you can phone Microsoft support line and retrieve 24 digit registration key. They will walk you through the whole process of re-activating the Office XP.

Microsoft will not issue another license key unless you purchase one. This will cost the same as buying one from a retail location.

Even if it was an OEM install, I don't think it's fair that you wouldn't be able to get back the key if something happened.
Without mentioning specific examples, there are program that let you view your office key, or you could just go through the registry if you know where to look. SO i imagine you have your own computer, or another one, with Office XP as well. Just use the same key.

Have you tried calling Microsoft?

You could have ringed MS for 1$ a minute maybe, but I would have emailed them to phone me, instead of wasting phone bills. If you can't get a key from emailing/ringing Microsoft. I'll doubt you'll get one unless you purchase, MS are too lazy to search a database with all the serial numbers maybe.

If it was preinstalled with your PC, check the computer and CD case for a COA with the Product Key. MAKE SURE IS SAYS ON THE TOP "MICROSOFT OFFICE XP"

xxxx-jozh-xxxx

Microsoft would have no idea what your product key was unless you have registered your software with them. It would be quite difficult to try to find out what the key was. Probably, you would have to purchase a new product key in order to reinstall the Office XP suite.