LEA doesn't ask, they hand court orders: Lavabit wasn't exactly "asked" for their SSL keys.
The certificates are not fake, they are real valid certificates the private key of which is not fake, just different one.
For that reason self signed certs should ideally be used only in testing, on in situations where you yourself can verify their authenticity.
• February 2, 2018 PM K15 - Self signed certificates should bring up a stern warning on your browser unless you unwisely turned this off.
"Theoretically it would work, but the thing is we get requests from law enforcement every day, and in entire time we have been doing this, we have never had a single instance where law enforcement asked us to do something inappropriate.