Heat oil in a large saucepan over medium-high heat. Add garlic and onion; cook, stirring occasionally, until tender, 1 to 4 minutes. Add lemon juice and cook for 1 minute. Add 3 3/4 cups cucumber slices, broth, salt, pepper and cayenne; bring to a simmer. Reduce heat and cook at a gentle simmer until the cucumbers are soft, 6 to 8 minutes.