To those who admonish others for going to the lav barefoot or in socks ... OMG, just stop that. Unless they are your actual children, you don't need to be their mother. Feel free to sit there in judgment of them, however, if it makes you feel better.
This coming from one who does wear socks to the lav - but only the throwaway socks provided by the airline in business or first on long-haul flights. Pretty much everyone does, and the lavs are generally pretty clean up front anyway.