Oh, that is so familiar. Does she read or at least look at books? Our policy was not to enforce lights out, but to enforce (earlier than 9) a staying in bed time; DS was pretty happy to comply provided he had a high enough stack of books. He had phases of wanting someone to come and lie down with him (sometimes very late, after he'd been reading for ever) at which point we'd usually do it, but on condition that he was lying still, not wriggling or playing. By the time he wanted that, he'd usually sleep quickly.
Very, very familiar!
We do a similar thing. I know that my LO has no idea how to rest and relax, in order to be able to go to sleep. Some children do this naturally. Mine don't. It took me ages to learn it myself, so I don't really expect that they would know it.
But I consider it my job to help them figure it out and get a good nights sleep. I also know the futility of trying to force a child to sleep!
We do a similar thing to Colin's mum. First we have a rule about being calm and quiet from a certain time. This is harder to enforce, but I really believe that they will learn to do this themselves (eventually!) if I keep modeling it. So after they come out of the bath, we have very quiet music on, DH and I speak softly, The house is closed up and dark, etc. Then they have to be in bed by 7pm, but when they go to sleep is up to them. He's not reading himself yet, so sometimes he likes to look at pictures, or listen to story CD's or music (chose carefully!) Meditation CDS can be good for this. Often, like Colinsmum, my LO will ask for someone to pat him, and we are happy to do that if he is lieing still and has his eyes closed, so usually he will fall asleep very quickly then.
Of course sometimes this all goes out the window!
