According to a recent thread on Reddit, Localbitcoins traders allegedly have to verify their identity if they are trading "significant" volume using the peer-to-peer platform.

Localbitcoins 'Error' Involves Know-Your-Customer Verification

Bitcoin users are frantically searching other exchanges today that don't require Know-Your-Customer (KYC) verification. A post on the Reddit forum /r/bitcoin on April 17 showed a picture that stated a Localbitcoins user's trade volume was "significant" this past year, and the trader had to verify their identity in order to keep trading. The picture reads:

Error! Your trade volume has been significant in the last twelve months. Please verify your identity to continue trading.

Localbitcoins does use a verification process but it's never really been enforced, although some believe more traders will trade with you if you are verified. Much like the rest of the exchanges out there that do require immediate verification, Localbitcoins uses an ID service called 'Netverify,' created by a company called Jumio. Basically, the user uploads a picture of both sides of their license or state ID and in a few minutes, the platform reveals if the identification is a legitimate or not.