Prepare a grill or large grill pan for medium heat. Quarter the tomatoes, then slice each quarter into 1/2-inch-thick pieces. Combine with 1/4 teaspoon salt in a medium bowl; let sit at room temperature.
Grate 3 of the garlic cloves into a 1-quart resealable bag. Add 1/4 cup of the oil, half the lemon zest and juice, and the chicken, and seal the bag tightly. Massage the marinade into the chicken, making sure it is evenly coated. Let sit at room temperature for 20 minutes.
Meanwhile, grate the remaining garlic clove into the carafe of a blender. Add the avocados, scallions, 1/2 cup water, 1/3 cup of the oil, the remaining lemon zest and juice, 1/2 teaspoon salt and a few grinds of pepper, and puree until smooth. Place a piece of plastic wrap directly on top of the dressing, and refrigerate the carafe.
Transfer the chicken to a plate or baking sheet, shaking off any excess marinade. Sprinkle liberally with salt and pepper. Place the chicken and the bacon on the grill. (Note: If you have a charcoal grill, cook the bacon in a grill pan. It should not be grilled over charcoal because of the risk of flare-ups.) Grill the chicken until charred on both sides and an instant-read thermometer inserted in the deepest part of each breast reads 165 degrees F, about 5 minutes per side; transfer to a cutting board, and let rest for at least 5 minutes. Grill the bacon, flipping as needed to ensure even cooking, until lightly charred on both sides and most of the fat has rendered, about 10 minutes; transfer to the cutting board.
While the chicken rests, quarter the romaine hearts lengthwise, leaving some of the stem attached to each quarter. Brush the cut sides with the remaining oil, and sprinkle liberally with salt and pepper. Grill, cut-side down, leaving 1/2 inch of space between each quarter (do not crowd; grill in batches if needed), until 1 cut side is lightly charred, 30 seconds to 1 minute; turn and repeat for the other cut side; transfer to a cutting board, and let cool slightly. Cut into 1-inch pieces, and mound onto a large platter.
Cut the chicken into 1/2-inch pieces, and crumble the bacon. Arrange the chicken, bacon, hard-boiled eggs, tomatoes (along with the juices) and blue cheese in rows on top of the romaine. When ready to serve, toss with the dressing, season with salt and pepper and serve immediately.
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