Coarsely grate potatoes and onion. Transfer to sieve; press out excess water. Transfer to large bowl; mix in egg and cornstarch, and season with salt and pepper.
In large skillet, add enough oil so that it’s 1⁄2-inch deep, and heat. Add 1 tbsp of potato mixture per latke, leaving 1 inch between each; flatten with back of spoon. Fry until golden brown on both sides, 4 to 5 minutes. Transfer to paper-towel-lined plates.
In bowl, stir together blackberries, vinegar and hot water; set aside. Place dill in large mortar, add sea salt and mash with pestle into a smooth paste. Scrape into bowl; stir in sour cream and season with a squeeze of lemon juice.
Using vegetable peeler, shave asparagus into thin strips.
To serve, top each latke with dill cream, slices of lox and 1 blackberry for “caviar.” Serve on platter with asparagus strips.