I'm not sure if this answer will be of much help but I've never had a lizard chase after me & I do enjoy feeding them especially at Crown Bay in St Thomas. They love the soft rolls from the buffet.
Be warned that they do bite if given the chance as I found out on the last cruise a few weeks ago. I was crouched down feeding one from my right hand when another saw the opportunity to grab the remaining roll from my left hand and grabbed my finger as well. Of course if I hadn't been feeding them they would never have even approached me.
Just don't feed them & you've got nothing to worry about.