I had to go today to get a replacement for my lost passport. I wrote a blog post about all the steps, so if anyone is interested or needs to do the same, you may want to check it out. http://socialmediabar.com/replace-lost- ... lima-peru1
This is also the process for stolen passports, or if you just need to replace an about to expire passport.
I didn't not mention in the article - If your passport is lost or stolen, you should immediately report it to the police here and get a copy of the police report, as well as notify the Embassy. It could keep you out of trouble if someone else gets up to no good with your ID.