Add the shallots and cook over low heat until softened, about 4 minutes.
Add 3/4 cup of the wine and boil over high heat until reduced to 2 tablespoons, about 7 minutes.
Reduce the heat to moderate.
Remove the skillet from the heat and whisk in the butter, 1 tablespoon at a time, occasionally moving the pan back to the burner to keep the sauce very warm.
Stir in the capers and season with salt and pepper.
In a large skillet, combine the water with the remaining 1/2 cup of wine and bring to a boil.
Season the salmon fillets with salt and pepper and add them to the skillet.
Simmer very gently over low heat, turning once, until just cooked through, about 4 minutes per side.
When the salmon is almost done, gently reheat the butter sauce over moderate heat, whisking constantly just until hot; do not let it boil.
Spread the shredded lettuce on plates.
Using a slotted spatula, remove the salmon fillets from the skillet and quickly pat them dry with a paper towel, then set them on the lettuce.
Pour the caper-butter sauce over the salmon fillets and serve.