Place dried chickpeas in a large bowl and cover with water by 2-3 inches. Soak 12-24 hours. Beans should be soft enough to crush between two fingers, but still firm.
Drain chickpeas and place in the bowl of a food processor along with the garlic, onion, cumin, cayenne, parsley, salt, black pepper, baking soda, and lemon juice. Pulse until everything is coarsely minced, stopping to scrape down the sides of the bowl as necessary. This should take about 30 seconds.
Preheat oven to 375°. Drizzle 2 tablespoons of olive oil onto a baking sheet. Form falafel mixture into patties, using about 2 tablespoons of mixture per patty. Place patties on the greased baking sheet, and drizzle with the remaining 2 tablespoons of olive oil. Bake 10-15 minutes per side. Falafel should be crisped and nicely browned.
Meanwhile, combine the tomato, cucumber, red onion, avocado, and salt in a medium bowl. Set aside.
Make the dressing by whisking together the yogurt, lemon juice, cumin, black pepper, salt, and cayenne. Set aside.
To assemble salads, divide lettuce between plates. Top with chopped tomato/cucumber/onion/avocado mixture, and place falafels on top of that. Drizzle with lemon-yogurt dressing and sprinkle with feta cheese. Serve immediately.