Blend all BBQ sauce ingredients into a puree. Keep refrigerated.
Season burgers with salt and pepper. Brush sweet potato and avocado slices with oil 2 tablespoons. Season with salt and pepper.
Brush grill grates with remaining oil. Place sweet potatoes over a medium-hot grill. Grill 8–10 minutes, until soft inside.
Meanwhile, grill burgers 3–4 minutes on each side. Do not overcook; bison is a less- fatty meat than ground beef and will dry out. During the last half of burger cooking time, place avocado cut-side down on the grill.
Scoop out warm avocado from skins. Mash and add lime juice; combine well.
To serve, place each burger on a lettuce leaf. Spoon BBQ sauce over each burger, top with sweet potatoes and a dollop of grilled avocado.