as far as negotiating rates while locked, just continue to shop for rates. if you find a better rate, let the original lender know. the worst thing that can happen is that they say no, and you decide to not refinance with them (may be a small sunk cost with credit check fee).

Thanks brg654.

I did follow zillow rates during the refi mostly in fear it wouldn’t close in time. Unfortunately and fortunately the rates were never lower. But it’s good to know for the future.