I am not a fan of leasing for folks rebuilding because if you lock in when your scores are not at their best your stuck with crappy terms for 3 years versus if you bought and put some money down to keep your LTV decent you could refinance as your credit improves. The answer to your question is that most captive lenders will lease to someone in the low 600's but with less than good terms (high interest) which cancels out many if not all of the payment advantages that leasing has over traditional financing. I have seen more than a few folks with low 600's or upper 500's lease for payments that were shockingly high, you see them all the time on swap-a-lease.
If you have experian auto scores of 670 BMW will put you in their upper tier for leasing, I have heard others have similar policies so one good way to find out is if you lock into a specific manufactuer go to an enthusist website and you are likely to find leasing tier information posted.
If you need a car now and you have plans of your credit improving consider a purchase and refinance. I bought as I started my rebuild in the mid 500's at 12.5% and was able to refinance to 4.29% after about 6 months due to improved scores, that saves us over 7,000 over the life of the loan.
