Who's Lily?

Lily is five and she's going to have her fifth birthday soon. She lives in Cambridge, but she's often standing right behind me. She's got a baby; although this could just mean a baby doll. She's also coming for tea most days - but never arrives. She's Beatrice's best friend and... yes... she's imaginary.

I'm not an expert on imaginary friends, but isn't three a bit young to start?