I would refer out purely because of the pain. Personal Training is very unregulated but my views in that case is - if there's sever pain (i.e. back spasm) or you can't train them pain free then you need to refer out.
Anyway, I have an ex gymnast as a regular client who has the classic gymnast spine - Excessive lordosis!! And a history of back (and knee) problems and when it hurts the pain is right where you describe it. She had a very unstable core and dominant lower back, also big discprepancy in side plank endurance. Very knee dominant. Sounds like everyone else, really, but it can seem more complicated than it is when someone has an athletic background. Very unusually, she loved lifting from the start!
I also have a client who has a back ground in Ballet, Jazz, Tap, etc and is also a Ballet instructor, part time - she's quite young (21). She also has minor complaints of back pain. She's a difficult one to get to embrace lifting, too!
One thing about Ballet and most forms of dance, but especially Ballet is everything is done way up on the toes. Remember weight lifting is one of the only "sports" where you're back on your heels - atleast for the most part. Gettting a Ballet dancer back on her heels will expose a world of weaknesses. This client is honestly amazing at Ballet, but a simple single leg glute bridge will cause a hamstring cramp because the glutes won't fire properly. The glutes are a big issue, and so is "anterior core" - that lower back will try and take over everything. You need to get the rest of the "core" really stable to take some stress off the lower back. In some cases she's extremely athletic and moves amazingly, and in others (glutes, "core"), I literally have 50+ year old women who put her to shame. The goal should be to prioritise the weaknesses.
Read this for the core stuff - http://www.t-nation.com/free_online_art ... training_1