If you have in fact lost your passport and you decide to get a new one before you trip. I would get started asap. Replacing a lost passport is a major hassle. My sister went through it a few years ago. If your passport is still valid, the State Department does not want it floating around out there. The view a lost US passport as a "serious situation."
My sister had to write a narrative explaining when the passport was last used, where it is likely to be, and everything she had done in order to recover it. This was in addition to the replacement fees. She then was issued a temporary passport, good for a year.
Of course, my sister is a bit of an airhead, and found her original passport about a month after she got the temporary one, but that's a different story....
Oh, and I agree with Deb, I don't leave the US without my passport, either.