Heat the grill to medium.
Place the strips of bacon on the grill (lay them across the grate so they don't fall through) and grill for 3 to 4 minutes on each side, until golden brown and slightly crispy. Remove the bacon to a plate lined with paper towels. Increase the heat of the grill to high.
Form the meat into 4 (8-ounce) burgers, brush with the oil and season with salt and pepper on both sides. Grill the burgers until golden brown on both sides and cooked completely through, about 5 minutes per side. Top the burgers with the blue cheese, close the cover, and continue cooking until the cheese begins to melt, about 1 minute longer.
Place the burgers on the bottom half of each bun and top with a slice of tomato, 2 slices of avocado, 2 slices of bacon and some of the dressed romaine. Cover each burger with the bun tops and serve.
Whisk together the vinegar, lemon juice, mustard, Worcestershire, garlic, sugar, salt, pepper and oil in a small bowl. Cover and refrigerate for at least 30 minutes before using to allow the flavors to meld.
Just before assembling the burgers, place the romaine in a medium bowl and toss with the vinaigrette.