Set up the sous vide water bath for 135 degrees F.
Remove the lobster tail from the shell by cutting along the middle and splitting the shell to extract the tail meat whole.
Place lobster tail, butter, and parsley leaves in recloseable or vacuum seal bag.
Vacuum seal using the Moist setting or using the water displacement method. The water displacement method helps the lobster meat retain its shape for optimal plating.
Place bag in the water bath for 30 to 60 minutes. Be advised that after 60 minutes, the lobster meat will break down and become mushy.
Quick chill the bagged lobster in an ice bath for 5 minutes.
While chilling the lobster, add all the cocktail sauce ingredients into a small bowl and stir to combine.
Prepare the cocktail glasses with lettuce leaves and the cocktail sauce in the bottom of the glass.
Remove the lobster from the bag and section the tail into bite sized pieces.
Place lobster chunks around the front edge of the glass.