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.
For the vinaigrette:
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.