Blend chickpeas together in a food processor or blender until they turn into a paste; transfer to a bowl. Mix onion, 1/4 cup parsley, eggs, salt, black pepper, and thyme into chickpeas paste. Add 1/2 of the oats and 1/2 of the bread crumbs.
Spread the remaining oats and bread crumbs onto a plate.
Form chickpea mixture into patties; press into oat-bread crumb mixture into completely coated.
Heat oil in a large skillet over medium heat; add patties and cook until patties are golden brown, 3 to 4 minutes per side.
Mix crab meat, mayonnaise, celery seed, sugar, and paprika together in a bowl until crab salad is well mixed.
Place a bed of lettuce on a serving plate; top with chickpea patties. Spoon crab salad on top of each patty.