Generally, once you've locked in a mortgage rate, the terms are fixed and usually cannot be renegotiated. However, some lenders offer a float down option, allowing you to negotiate mortgage rates if market conditions shift favorably during the rate lock-in period.
A mortgage modification changes the terms of your original mortgage agreement. Your lender will work with you to try and find a way to lower your monthly payment by adjusting the terms of your current mortgage. The goal is to help you get back on track.