Step 1: Rinse the trout, inside and out, under cold running water, then blot dry, inside and out, with paper towels. For each trout, place two pieces of butcher’s string about 3 inches apart on a work surface and lay down a piece of prosciutto. Stuff the trout with dill sprigs and lemon slices and season with salt and pepper. Lay a slice of prosciutto on top of the trout, bring up the ends of the strings, and tie the trout crosswise in two places to secure the prosciutto and keep the stuffing inside. Brush oil on the outsides of the trout.
Step 2: Set up the grill for direct grilling and preheat to medium-high (about 350 degrees).
Step 3: When ready to cook, place the trout directly on the grill grate. Grill the trout until nicely browned on the outside and cooked through, 6 to 10 minutes per side. To test for doneness, insert a slender metal skewer into a trout for 20 seconds: It should come out very hot to the touch. Serve with Mustard-Dill Sauce.