Cut 2 pieces of parchment paper about 12×15 inches. Place them into the slow cooker lengthwise, one on top of the other, to create a sling that will make it easy to remove the salmon later.

Slice 2 of the lemons into 1/4-inch thick slices. Cut the remaining lemon into 4 wedges and set aside. Arrange the lemon slices in a single layer along the bottom of the slow cooker, on top of the parchment. Top with the parsley sprigs and shallot slices. Pour in the wine, and just enough water to get the level of the liquids even with the lemon, about 1/4 cup.

Season the salmon with the salt and pepper to taste. Place the fish onto the lemon slices.

Cover and cook on low for 1 to 1 1/2 hours, until the salmon is opaque throughout.

Using the parchment paper sling, transfer the salmon to a baking sheet. To serve, gently transfer a piece of salmon onto each of 4 plates, discarding the liquid, lemon, and herbs. Serve topped with the capers and with the reserved lemon wedges for squeezing.