In a mixing bowl, whisk together the mayonnaise, lemon juice, chopped fresh dill, and freshly ground black pepper until smooth.
Refrigerate the lemon-dill mayonnaise until ready to assemble the sandwiches.
Place two slices of bread on a work surface. Spread a portion of the lemon-dill mayonnaise on the inside of each slice.
Top one slice of bread with lettuce leaves and half of the smoked salmon, then close with the second slice of bread to form a sandwich.
Repeat to make the second sandwich with the remaining bread and salmon.
Heat a panini press and lightly press each sandwich until the bread is golden and warmed through, about 3–5 minutes.
Remove from the press, slice if desired, and serve immediately.