Pre-heat oven to 400f degrees and line a large baking sheet with parchment paper.
Slice eggplant in ¼ inch slices and coat with a bit of olive oil and season with sea salt on the baking sheet. Bake in a single layer (slices can touch each other a bit for more room) and roast for approx. 30 mins. until cooked and golden, flipping half-way.
Meanwhile, add 2 Tbsp olive oil to a large skillet and heat over medium. Add the ground lamb, seasoning with the salt, paprika, and cinnamon and breaking up with a wooden spoon until browned on all sides and liquid from the meat is evaporating, approx. 10 mins or so. Remove meat from the pan and set aside, leaving fat/oil in the pan (or adding more if needed).
Next, add the chopped onion and mint, continue to saute while seasoning with salt until translucent, approx. 5-8 mins. Add garlic last (be careful not to burn it) for a few minutes. Then add in the tomato paste, stir around the veggies and lastly add your wine or bone broth, stirring occasionally for 3 minutes.
Add tomatoes and break up with a wooden spoon into small pieces. Add lamb back in, stirring occasionally until most of the liquid is evaporated and mixture looks like a thick meat sauce, 5–7 minutes. Set aside and make the bechamel sauce.
Dairy-free Cauliflower Bechamel Sauce
In a pot, steam cauliflower florets with boiling water until it's tender when pricked with a fork (approx. 8 mins.).
Meanwhile, add coconut CREAM (not milk), nutritional yeast, and lemon juice to a high-speed blender.
Separately, take 1/2 cup of water and add arrowroot flour to it. Stir it around to create a slurry. It will thicken slightly in the cup, make sure it's stirred well with no clumps at the bottom. Once that's mixed well, pour HALF into the blender. Save the other half in case you need it (depending on how large your baking dish is, you might want more liquid).
When cauliflower is ready, add it to the blender, season with salt. Blend everything for a minute or so, until a thick sauce has formed.
Grease an 8x8 baking pan with olive oil. Layer half of eggplant in pan, covering the bottom entirely. Spread half of lamb mixture over eggplant in an even layer. Repeat with remaining eggplant and lamb to make another layer of each. Top with cauliflower béchamel and smooth surface.
Bake moussaka on a middle rackin the oven until bubbling and béchamel are browned in spots, 30–45 minutes. Let cool 30 minutes before serving. Serve or store in the fridge or freezer.