What is the relationship between Dan and Lucy?

M: Hello, Super Smart Customer Services, Dan speaking. How can I help you?
F: Hello. I ordered some gifts last week from your website, but the delivery is completely wrong!
M: Oh dear! What’s your name, please?
F: Lucy Smith. Well, firstly, I ordered a Robbie Williams CD but I got a Coldplay CD. I also ordered a black backpack, and I received a pink handbag.
M: Oh...Well, pink is the colour right now, isn’t it? I have a pink handbag myself.
F: Yes, but it’s my brother’s birthday present. I don’t think my brother wants a pink handbag for his birthday! Listen, the order is wrong! Some things are missing, too.
M: OK, I’ll send some new ones out to you in Manchester.
F: Manchester? I live at 33 Aintree Avenue, Brighton.
M: I’m really sorry. Oh, I see, there’s another Lucy Smith living at 21 Wellington Gardens, Manchester. That’s why you got the wrong order! OK, the correct order is on its way to you right now.