Make tartar sauce: combine mayonnaise and Greek yogurt in a small bowl. Mix thoroughly to combine. Stir in the remaining ingredients. Chill until ready to serve.
In a large bowl, mix together the crabmeat, lemon juice, breadcrumbs, egg, yogurt, mayonnaise, scallions, mustard, and salt and pepper to taste. The mixture will be a bit wet.
Gently shape into 4 patties; place on a plate. Cover with plastic wrap and refrigerate for at least one hour.
Heat the grill to medium-high heat, and brush with canola oil. (If your grill has wide grates, you may want to cook the crab cakes in a skillet on the grill). Cook the crab cake patties until golden, about 3-5 minutes per side.
Serve on toasted burger buns with tartar sauce, lettuce, red onion, and fresh lemon wedges.