A mandoline or other adjustable-blade slicer is the best tool for slicing the radishes and celery paper-thin, but a very sharp chef's knife will also work.
Combine 2 cups water, lemon slices, 2 tablespoons brine, and 2 teaspoons coarse salt in a medium pot; bring to a boil. Add shrimp and return to a boil, then immediately remove from heat. Let stand until shrimp are opaque throughout, about 1 minute. Remove shrimp with a slotted spoon; let cool completely.
Halve shrimp lengthwise and toss with pickles, remaining 3 tablespoons brine, oil, radishes, and celery in a large bowl.
Stir garlic into mayonnaise, then spread on bread slices. Top with shrimp salad. Sprinkle with flaky salt and dill; serve.