If doing a Lightworker Healing Protocol session for a non-believer, is it best NOT to tell them?

The situation you describe calls for special care and consideration. People will rightly feel insulted if you go against their wishes whether you are doing an act that is truly bringing a divine blessing to them or not. If you choose to help someone without their awareness, and especially so if it has been discussed and permission denied, it is not wrong to proceed because there is a higher good and a higher counsel that can be attained before anything is actually carried out by the divine realm. But on a personal level, human to human, it would be best to be an unsung hero and quietly request assistance for whatever is highest and best for that person and not bring it to their attention that you did something behind their back. This, in effect, is a kind of situation where you may, through silence, be creating a "white lie," but that is not a violation when the intention is the greater good and you are doing something that is selfless in motivation.