Mix ground beef, half the onions, bread crumbs, pepperjack cheese, and eggs in a bowl; form into 12 patties.
Combine tomatoes, half the remaining onion, cilantro, half the serrano chile pepper, and half the lime juice; mix well to make pico de gallo. Cover and chill in refrigerator.
Mash avocados, remaining onions, remaining serrano chile pepper, and remaining lime juice together in a bowl to make guacamole. Season with salt and pepper.
Heat a skillet over medium-high heat; pan-fry burger patties to desired doneness, 3 to 5 minutes per side. An instant-read thermometer inserted into the center should read 160 degrees F (70 degrees C).
Assemble each sandwich by placing a burger in each bun; top burger with guacamole, shredded lettuce, and pico de gallo.
