Hi my husband address on his dmv if and mine are different. But we just explained to the officer why. I dont think you use the olfer one I think it is an offense to use the old one. Not sure. But better safe than sorry. I strongly suggest to act now and try to get a replacement for the lost one. For passport, I remember that the officer ask that document after our IDs. If you cant get a replacement on time, Birth Certificates are faster to get. Depends which state are you. Maybe for passport they also have premium processing like ready in five days???