In a medium bowl, whisk together the mayo, cocktail sauce, and fresh lemon juice until smooth and well combined. This creates your flavorful base that will bind everything together. Set aside while you prepare the other components.
In a separate bowl, gently toss together the shrimp pieces, chopped celery, and dill pickle relish. Sprinkle the Old Bay seasoning over the mixture and fold everything together until evenly distributed. I find that gentle folding rather than aggressive stirring keeps the shrimp from breaking apart and maintains a better texture in the final salad.
Pour the dressing mixture from Step 1 into the shrimp mixture from Step 2 and fold gently until all components are evenly coated and combined. The dressing should coat everything without being soupy. Taste and adjust seasoning if needed.
Divide the crisp lettuce among serving plates, creating a bed for the salad. I like to use a mix of romaine and butter lettuce for both crunch and delicate texture. Spoon the shrimp cocktail salad generously onto each lettuce bed and serve immediately while everything is cold and fresh.