luke lazarus was convicted of raping an 18-year-old at soho nightclub .
the 23-year-old sydney man was sentenced to a minimum of three years .
he then bragged about it to a mate via a text message next day after attack .
lazarus ' lawyers are now appealing his conviction .
this comes as waverley mayor sally betts wrote a reference for him .
liberal mayor asked for him not to receive a custodial sentence .
says she is trying to ` close loophole ' of ` risky behaviour ' in young women .