Preheat grill to medium-high. (If you are using a charcoal grill, coals are ready when you can hold your hand 5 inches above grill for just 3 to 4 seconds.)
Whisk lemon juice with mustard. Add oil in a slow, steady stream, whisking until emulsified. Whisk in salt and pepper. Toss pears with 2 tablespoons dressing.
Grill sausages, turning frequently, until heated through, 10 to 12 minutes total. At the same time, grill pears until softened and lightly browned, 4 to 5 minutes per side. Top sausages and pears with thyme, and serve with chutney, mustards, and remaining dressing.