In a medium saucepan, combine water, lemon slices, tarragon sprigs, and salt. Bring to a boil over high heat. Remove from heat. Add shrimp, and let poach until shrimp are opaque and pink, approximately 5 minutes.
Transfer shrimp to a large bowl filled halfway with ice, and let cool.
In a small bowl, combine mayonnaise, chopped tarragon, lemon juice, lime juice, celery, shallot, salt, and pepper, whisking well.
Drain shrimp, and blot dry with paper towels.
Place shrimp in food processor, and pulse until finely chopped. Add mayonnaise mixture, pulsing to combine. Transfer mixture to a covered container and refrigerate until very cold, approximately 4 hours.
Spread shrimp mixture evenly onto 4 bread slices. Top each with a remaining bread slice.
Using a serrated bread knife in a gentle sawing motion trim and discard crusts from sandwiches. Cut each sandwich diagonally into 4 triangles.
Serve immediately or cover with damp paper towels, place in a covered container and refrigerate until serving time.
Recipe by TeaTime Magazine at https://teatimemagazine.com/tarragon-shrimp-sandwiches/