You probably didn't get it, what I mean is probably your loan didn't get approved in PROCEDURE, so you probably cannot sue them because you don't have the documents needed.
We're direct lender(correspodent) too so I know all the procedures. LA could be similiar too and we also have branch there.
When you apply for a loan, the bank doesn't have to approve your loan, you need to provide necessary documents. I've incurred the requirement for proof of 3+ years consecutive income for a sound reason.
From your writing, the escrow file you signed is critical, If it is original application(I suspect), then looks like they didn't "officialy" underwriting your loan until after December 9, and Mid Jan requirement could be when they actually look at your loan and ask for this documents(whether this is an excuse or not, is another story) since you cannot provide this, so this loan cannot be approved. Legally, no problem on bank side with this proccedure.
If the escrow file you signed is closing documents(with a closing agent, could be an attorney, verified your Ids)then your loan should be already closed, unless you have big issue happen after signed the documents, like losing job, etc.