I mostly agree with the other posters. Lending money so he can buy his girlfriend something is something that you shouldn't have to do. Although- i've apparently not have the negative experiences other people have had with family and money. I've been in trouble before, and family has lent me money. I was young and stupid. I'd be willing to do the same for them now that i'm in a better place. I couldn't imagine charging family interest, or getting contracts or liens involved. But every family is different.
Personally, I would say no, but find a way to make it a constructive rejection so to speak. Personally, I'm very close with my brother, who is younger than me, and I want him to always think that he can come to me with whatever problem or issue he has, money or otherwise. The last thing I would want to do is alienate him, and make it so that he never thinks that he can come to me with a problem. (no matter how ridiculous I might think the current problem is) I don't know anything about your brother or how old he is, but I could see my 19 year old brother potentially making a similar request of me. Of course, I'm not going to do it. But he's 19! I mean, i certainly wasn't mistake free when I was 19. He might be really convinced that he needs to do this for his girlfriend, I don't know. But I would try not to automatically scoff at it, and make him feel like a moron for bringing it up. I would sit him down, let him know that you don't have the money for something like this, but above all make it a constructive conversation. He might be upset for awhile, and angry- but that's ok.