@Meekspees It would take an "Asimov law" type restriction that physically prevents him from telling a lie when the purpose of the lie is solely to grow his nose.
But he could justify it that way after-the fact.
"Hey, can you make your nose grow on command?"
(Intending to actually lie) "Of course I can!"
<nose grows, Pinocchio gets a little worried> "Uhβ¦. See!"
But he'd only be able to do it once. Because future attempts would be "purposeful" and he couldn't say it.
@Meekspees (I may think about logic puzzles a bit too muchβ¦)