Hello FiscalCliff. You don't get much more shy than my boy. He was very poorly as a young pup - and unfortunately contagious to other dogs. We carried him everywhere for socialisation, but he ended up terrified of other dogs, from lack of interaction.
When we first started puppy classes he just hid behind my chair and refused to even look at the room. The trainer was well aware of his start in life and arranged for us to be seated with a wide area of space around us and for the first couple of lessons I just click-treated every time he came out from behind the chair or looked at another puppy/dog. By week three he was out in front and taking part in the training. Today he has been playing dafties with his favourite love interest - a super cute and wriggly, 5 month old Cockerpoo girl. 
He's still very nervous of other dogs out and about, but is brave enough to approach quieter dogs for a gentle hello these days and is improving all the time. I'm sure he would never have reached this point without puppy classes.
I would wholeheartedly advise anyone with a puppy - of any breed - to find a suitable puppy class. It helps build a bond between you and the pup and is such valuable socialisation - even if they aren't going to be the world's best obedience champion, those benefits alone make it really worthwhile. If you can find somewhere where the trainers are aware of how sighthounds are different, it will definitely help, but it's not essential.
I would say puppy classes will actually build her confidence. Pip has absolutely blossomed at his and as I said, he was terrified at first.
It's not that I don't think training classes are right for Lurchers, more that some crosses might not be predisposed to traditional obedience, iyswim - that's not to say they wouldn't benefit from going though. I do think every single Lurcher pup should to to training classes - training a good recall alone is a good enough reason and of course a good bond, which you will also build through training, will also make your dog more keen to come back to you.
Even better, it really wears them out. We got home at 1.00 ish this afternoon and Pip has been totally zonked out in his crate all afternoon. Didn't even stir when I went upstairs, whereas he usually waits behind the living room door and whinges after me. He did wake up long enough to stuff down his eggy kong (which lasted him an hour, so that was a result ) during the school run, but went straight back to sleep afterwards and has been asleep ever since.
Whippet/greyhound/Beddie is a nice cross, Beddie always makes the mix interesting and fun! Do you have any photos of her?
Pip is rough coated and we don't know his exact cross because he was left in the gutter at the side of a road with his sister at less than 24 hours old. As he's grown he's clearly got the Saluki figure and best guesses are that the other dominant breed is terrier of some sort. He looks very like a Parsons Jack Russell in the face sometimes, but his legs are so long, I can't believe that's a first cross in his case. Some people on Lurcher Link have said they reckon he might have some Collie in there somewhere as he's pretty sharp - for a Lurcher!
There are some pictures on my profile, although they're quite a bit out of date (I really need to get around to putting some more on). He's 7 months old, really leggy and 24 inches to the shoulder - so taller than my other Lurcher who is 8 years old, 23 and a bit inches and a Deerhound/Saluki x Whippet/Collie.
Speaking of Lurcher Link - definitely join if you can. They are lovely people and there is a wealth of Lurcher specific knowledge and experience on there. Mistlethrush and a couple of others from the pointy hound thread are on there and so am I.
Excuse the long post - I'm very excited to have another pointy pup coming to the thread. 