Combine the mint, wine, lemon juice, and honey in a mixing bowl. Add the lamb and onions, and toss to mix. Cover, and refrigerate 4 hours to overnight.
Preheat an outdoor grill for medium-high heat, and lightly oil grate.
Strain the marinade from the lamb into a small saucepan; set aside. Thread the lamb and onions onto the skewers, using 3 onions per skewer. Cook the skewers on the preheated grill until the lamb has cooked to your desired degree of doneness, about 8 minutes for medium-well.
Meanwhile, bring the reserved marinade to a simmer over medium heat. Whisk in the apricot preserves until dissolved, then reduce heat to medium-low, and simmer gently for 5 minutes, adding water if needed to keep the sauce from burning. Dissolve the cornstarch in 1 tablespoon of water, and whisk into the sauce to thicken; simmer the sauce 30 seconds longer. Serve with the lamb skewers.