Preheat oven to 400 degrees. Peel onions and cut in half and cut off ends. Slice thin into strips. Place into 9x13 baking pan. Add whole cloves of garlic and olive oil. Toss together.
Bake in preheated oven for 15 minutes and then stir. Bake for another 15 minutes and then stir again. Bake for about 10-15 minutes until the onions have softened but only barely turn golden. Remove from oven and let cool completely.
Remove garlic and smash with a spoon or flat size of a knife. Add to a medium bowl. Dice cooled onions and place in bowl, along with salt, lemon juice, and cayenne. Mix together and adjust seasoning as needed.
Serve immediately or chill until serving time. Serve with ruffled chips and/or crudité veggies.