In a large mixing bowl, combine the Brussels sprouts, leeks, eggs, flour, lemon zest and juice, and salt. Stir until the flour is fully incorporated.
Heat a thin layer of coconut oil in a large skillet over high heat. Prep a plate or baking sheet with paper towels.
Arrange a layer of Brussels sprout latkes in the hot oil, 1-tablespoon of batter per. Gently flatten the scoops with a flat metal spatula. (You just want to make sure the top is flat for when you flip.) Cook until browned and very crispy on the first side, about 1 to 2 minutes. Carefully flip and repeat on the second side, adding more oil as necessary. Remove to the paper towels to drain. Continue cooking the latkes in batches until the batter is all gone.
Meanwhile, make combine the ingredients for the aioli in a small food processor and puree until smooth. Transfer to a serving bowl.
Season the latkes with salt and a squeeze of lemon. Serve alongside the anchovy aioli, tahini yogurt, or your sauce of choice.