First off the lender does not generate the HUD, escrow generates the HUD. So you need to make that request to escrow not your lender.
Second off, the final HUD is never ready until the day that the closing occurs due to proration calculations.
Third off, escrow should always be able to give you a preliminary HUD prior to close of escrow based on an estimated closing date.
A more accurate version of the estimated HUD can be given after loan docs as the dates are less likely to move and the full lender fees have been given to escrow by the lender. Additionally if there are escrow accounts for homeowners insurance and property taxes, any estimates made by escrow for funding of these accounts is usually moot until after the lender has received loan docs and updated escrow to what these amounts should be.