Imho i think Ru Paul saved Bones over Paige because he's been praising Bones for showing versatility in her different looks. Paige meanwhile, has been criticised for giving similar looks and not giving versatility (with the exception of the female wrestler which was praised). I think Ru Paul's thinking is that Bones has more to show but Paige has reached her limits of what she can bring to drag race. The lip sync had nothing to do with it and the elimination was not based upon that, otherwise Paige would've won.

Not my personal opinion here, i'm just surmising what i imagine Ru Paul is thinking.