Like all clones, he has an inhibitor chip implanted to ensure absolute obedience to Order 66 when the time finally comes to execute it. However, Cut Lawquane had deserted the GAR and so most probably not present when the order was given.
If he ever encounters a Jedi thereafter, how will he react? Will the inhibitor chip activate?
Exact mechanism for activating Order 66 protocol in inhibitor chips is not described either in Canon or Legends. However, we know few things: it was activated by voice command, presumably over encrypted secure channel. Legends assume it could be activated only by Chancellor (Palpatine) although there is no confirmation for that in Canon. Palpatine, of course, could not contact each and every Clone commander personally, and each and every clone even less so. Therefore we could assume Order could be relayed down the ranks, although exact mechanism, as mentioned before, is not known. Somehow, effects of Order 66 were immediate . For example, Commander Cody, after receiving Order, ordered unknown trooper(s) to fire at Obi-Wan and was obeyed instantly.
As for Cut Lawquane, we know he was not inside GAR structure when Order was issued. I doubt Palpatine knew or cared about him, and would not have any reason to contact him personally. Cut didn't have GAR communication equipment with him, and was not part of any GAR communication network. He didn't wear standard issue helmet, so Order could not be transmitted to him that way. Only other way remaining would be if inhibitor chips themselves acted as receivers, but I doubt that, otherwise Palpatine would not need to use holoprojector to contact Cody and others.
Therefore, most likely, Order 66 protocol was not activated inside Cut Lawquane's inhibitor chip. He would not attack Jedi if he saw one . Although Order 66 most likely remained standing for years after it was initially given(to hunt down surviving Jedi), as far as we know it was not repeated. So, clones not affected by it immediately were not affected at all.
Clone Protocol 66 was an order implanted into the clones by the Sith Lords and Kaminoan scientists who created the clone army.
The Inhibitor Chip limited independence and aggression in clone troopers and ensured obedience to directives. The chips, however, were also created for another purpose. Namely to force the clones to comply with the execution of Order 66.
This is slightly confusing since in Canon CT-5385 ("Tup"), had a violent reaction to the chip malfunctioning without receiving the order.
CT-5555 ("Fives") had his removed for testing with no apparent effect. We also find out in Rebels that Rex, Wolffe, and Gregor all had their chips removed as well. None of them tried to kill Jedi despite receiving the order.
So it is clear that:
The obvious conclusion is that the chip (plus order) causes the violence. But it's called an "inhibitor" chip which implies the violence is always there and the chip prevents it. And then the Canon Wookieepedia entry says it does nothing more then force the Clone to follow the order. So something is not lining up somewhere.
But to come back to your original question, it is unlikely that Cut would kill Jedi since he deserted before Order 66 was issued (thus showing an independent streak that the chip was supposed to suppress anyway) and probably never received the order.
Since the chip is voice activated, any clone who was off comm channels or did not orally receive the order in some way (like Cut Lawquane) logically would not execute the order even if they met a Jedi afterwards. The chips' protocol for the activation of Order 66 would be dormant until he heard the command given.
To revisit: Order 66 only gives instruction to execute all Jedi and any other members of the army who violate Order 66.
However. Clones still had free will about other orders they were given. Of course, a clone who fully believed the story that the Jedi attempted to take control of the Senate and Republic would probably fully support the end of the war and reorganization of the galaxy into the Empire and continue to serve in the army. It is shown in The Clone Wars – Season 4, Episode 10 "Carnage of Krell" and The Bad Batch - Season 1, Episode 12 "Rescue on Ryloth" particularly, among many other examples from throughout the animated Prequel shows, that the clones have a sense of "right" and "wrong", a conscience, a moral compass, call it what you want. If a clone who, with his inhibitor chip still intact, came to believe personally that what the Empire was doing was wrong, he could go AWOL if he chose. Examples: Captain Howzer, Commander Cody, Captain Gregor, and possibly Commander Wolffe (remains to be revealed but I think is likely as he was seen with the rogue clones in The Bad Batch Season 3 trailer). However, it's hard to say whether or not a clone deserter with his chip still intact would continue to comply with Order 66 involuntarily if ever confronted with a Jedi. Even if the Order came from a political system that he wasn't loyal to anymore, would that matter against the programming that was never deactivated by the chip's removal? I don't believe so.
