In small sauce pan, heat 1/4 c water. Bring to a boil, then add salt and sugar, and allow to dissolve before adding vinegar and mint. Reduce heat to medium low and stir mint until it wilts and reduces. After about 4 minutes, reduce heat to lowest, add cover, and allow flavors to infuse.
Coat a large sauté pan with olive oil, toss in the diced onions, oregano, figs, and seasonings; coriander, cardamom, cinnamon, salt, and pepper. Bring the pan to medium-high heat and cook for about 5 minutes. Add the garlic and cook for 2 to 4 more minutes. Reduce heat to low and continue cooking until the figs melt into a jam-like consistency. Remove from heat and allow to cool.
Heat a separate pan on medium low heat, then add almond meal. Allow almond meal to brown, and toast slightly for 3-4 minutes, and then remove from heat and allow to cool.
In small bowl, combine veganaise (or regular mayo), garlic powder, lemon juice, lemon zest, and salt and pepper. Set aside.
In a large bowl, combine the lamb, the cooled onion and fig mixture, one egg, the almond meal, and additional spices; cardamom, coriander, cinnamon, salt, and pepper. Mix together thoroughly. Make a small "tester patty," to cook and test for flavor (like if it needs additional salt and pepper). Divide meat into about 8 even balls. Using your hands, lightly press meat into even, 1-inch thick patties.
Place on broiling pan, and broil in oven on low for 6-7 minutes each side. The tops of the patties should caramelize and brown slightly.
Broil both the buns with olive oil until they are golden, then broil the onions with olive oil, salt, and pepper until they caramelize—about 3 minutes each side.
Serve burgers with aioli, mint, arugula, onion, and cucumber.