Yes, all lenders which are privately owned corporations have the right to set their own internal guidelines that coincide with government sponsored loans like the FHA minimum credit score requirements. Most lenders also have compensating factors that allow for lower credit scores such as cash on hand, assets and or loan to value.
It is going to be hard to find which lender has the lowest score unless you just do the research and call around quizzing loan officers at various lenders.
I also alerted your question to LoanSafe's mortgage expert and forum sponsor, Erik Sandstrom with Prime Lending. He is active in the business and will let you know his opinion and what his lender requires.
Most lenders will start at 640 when it comes to FHA financing but very rarely will you run across a lender that goes down to 580. We are able to go down that low as long as you pass the automated underwriting system. For example, if you have a decent amount of equity in the home, a low debt-to-income ratio you're most likely going to get approved through the system but you'll never know until running it.
I work for a federally chartered bank that operates under very minimal to no overlays on government and conventional loans. We allow down to 620 in most cases but just last week I funded a loan at 610. Usually there are ways to improve you credit by doing minor items on revolving debt if you have small credit cards. If you have no debt to work with it can make it more difficult to improve the score.
As lenders we are able to run a system that will allow us to predict what you can do to increase your credit score rather than going to a credit repair company that will just dispute every item on your credit report.
If you would like me to run that system, I am able to originate loans in 46 states and I would assume you're part of that. Feel free to reach out to me directly at: Erik.Sandstrom@PrimeLending.com or 619-379-8999, you can also apply online at: www.LoansReduced.com