PREHEAT the oven to 225º and line a baking sheet with a wire rack. In a medium bowl, toss the eggplant with the liquid aminos, brown sugar, liquid smoke, maple syrup and cayenne pepper to coat. Let marinate at room temperature for 30 minutes, then drain and arrange on the wire rack, making sure the eggplant strips do not overlap.
DRY the tray of eggplant in the oven until crisp, 1 hour and 15 minutes to 1½ hours. Transfer the dried eggplant to a plate to cool.
MIX the vegan mayonnaise with the lemon juice in a small bowl, until smooth, then season with salt and pepper.
LAY three slices of toasted sourdough on a cutting board and spread each with some of the lemon mayo. Place two slices of the tomato and a few slices of the eggplant bacon, radishes and onion on the sandwich. Pile some frisée over the vegetables and top with another piece of toasted sourdough spread with the lemon mayo. Slice in half and serve.