Put the lemon juice and 1/4 cup olive oil in a small bowl. Season with salt and pepper and whisk to combine. Set aside.
Heat 1 tablespoon olive oil in a cast iron skillet over medium-high heat. Add the cactus, season with salt and pepper, and cook, turning, for 5 minutes. Add the chickpeas and cook for an additional 1 minute, stirring. Remove from heat.
Put the avocado, tomatoes, half of the onions, lemon zest, and cilantro in a medium bowl. Add the cactus and chickpeas. Drizzle with the lemon juice and olive oil mixture and gently toss to combine. Arrange the remaining onion slices over the top, garnish with the cilantro, and season with a small amount of salt and black pepper. Serve immediately.