If you find your lost passport after you have started the replacement process, that passport is considered cancelled and is no longer valid for travel. As soon as you have filed the DS-64 form, the State Department will cancel the passport you lost. This is a safety procedure so that if someone else finds your passport, they can not use it.

If you lose your passport overseas, you will need to go to the nearest US consulate to have your lost passport replaced. All of the same requirements for getting a lost passport replaced will apply.