Preheat the oven to 400°. On a rimmed baking sheet, toss the onions with 2 tablespoons of the olive oil and roast until softened, about 20 minutes.
Meanwhile, in a small bowl, whisk the mayonnaise with the lemon juice. Gradually whisk in the remaining 1/4 cup of olive oil and season with salt and pepper.
In a large skillet, cook the bacon over moderately high heat until crisp. Drain on paper towels and break each strip in half.
Light a grill or preheat a grill pan. Form the ground meat into eight patties. Season generously with salt and pepper and brush with olive oil. Grill over moderately high heat until well-browned on the bottom, 5 minutes. Flip the burgers, mound the brie on top and grill for 4 minutes longer, until the cheese is slightly melted and the burgers are medium-rare.
Spread the lemon mayonnaise on the cut sides of the buns; set the burgers on the bottoms and top with the bacon and onions. Close the burgers and serve right away.