Prepare all ingredients as listed.
In a small bowl, mix the ketchup, mayonnaise, and mustard until smooth to create the sauce. Set aside.
In a bowl, combine the ground beef, Worcestershire sauce, salt, and black pepper. Mix gently until just combined, then form into patties.
Heat a skillet or grill pan over medium heat. Cook the patties, flipping once halfway through cooking. During the final minute, place a slice of cheese on each patty and allow it to melt.
Toast the hamburger buns cut side down in the skillet or on the grill until lightly golden.
Assemble the cheeseburgers by spreading the sauce on the inside of the buns. Layer with butter lettuce, tomato, the cheeseburger patty, and red onion, then close with the top bun.
In a glass or pitcher, combine the sparkling water, lemon slices, and chia seeds. Stir well, allow the chia seeds to hydrate briefly, then stir again to prevent clumping.
Serve the cheeseburgers with carrots and hummus alongside the lemon chia sparkling water.