General assumptions: It would be good to eliminate Luke Wheeley after killing Mason, especially that he can be found in the near of Lenny a person who should be eliminated at the end.
Luke Wheeley spends most of the time on the barbershop ground floor. Do not try to attack him when he is surrounded by other armed characters. You can make your move once he gets to the corridor near the main entrance (screen above).
If you want to get rid of Wheeley in more original way, you can kill him using the explosion of gas stove. The gas stove is located on the ground floor and no one will react if you try to turn it on.
After turning it on, it is best to withdraw to the corridor located at the main entrance to the building. Wait until Wheeley approaches the stove and shoot it with the pistol. If youve done everything according to the plan, your target should die because of the explosion.
The least obvious and not recommended way of murdering Luke is waiting until he gets to the courtyard and stops at the barbecue. You can them aim the gas cylinder. It is best to do this from one of the rooms of the barbershop first floor, reducing the risk of exposing Agent 47.