The first thing to say about lurchers is that their temperament depends on their cross, so anything I say is a generalisation. A lurcher is a cross between a sighthound (not necessarily a greyhound) and another breed (usually working).
In general though, they (particularly saluki crosses) are almost cat-like in comparison to other dog. They are more independent - not that they don't want your affection, but they will think for themselves rather than look to you for instructions. This makes sense for sighthounds as they are bred to work at some distance from their owner without the owner's input. Typical training classes might not be a good fit for them - if you ask them to sit, lie down, and sit again they might just think that you're being ridiculous, go on strike, and settle down for a snooze.
They can be very sensitive. Harsh handling, raised voices, etc, are even less advisable than with other breeds. They will switch off, shut down, and be very stressed. They might not do well in noisy households particularly if there are regular arguments.
Prey drive is something you need to be very aware of. Some lurchers will chase anything
and they are so fast there's a good chance of catching it. Or of chasing it a couple of miles and across a road... It is a very rare lurcher who can be recalled once they have taken off after prey. Mine only really takes off after deer and rabbits. He has really good recall for a lurcher as I've had him from 7 weeks and he's a Mummy's boy and very food oriented (lurchers can be picky), but if he's got a deer in front of him I don't even bother blowing the whistle. I just wait for him to come back in his own good time and then check for wounds. Oh yes, lurchers have very thin skin and some are regularly down the vet's getting stitched up.
If they get sufficient walks (some people say they just need a couple of 20-min walks a day but that's very rarely the case - most days mine gets at least 2 hours) they are very quiet round the house, often only really moving to eat, or shift to the sunny spot. (Or they might just whine because the sun has moved and they want you to move it back again.) You won't be presented with a soggy tennis ball ten minutes after you get in for a walk! (Obv. this won't apply to puppies though.)
Compared to some dogs they are undemonstrative in that they don't have a tendency to jump on you and lick you to death (though a friend's saluki x has done this to me). My dog will come and rest the top of his head against my leg, and sigh. This for him is a special moment, an expression of love.
It's great that your daughter is so good at reading dog body language
It's a skill you can develop, particularly if, when you have a dog, you listen
. So many people don't, and as a result the dog will give up communicating, and you don't know what's going on in their head.
I've gone on a bit - I'm a lurcher nut
But you really need to read this: http://greydogtales.com/blog/?p=145
It's tongue in cheek, of course, but scarily true