Make sure tofu is really well pressed. You want these bites to be firm so they'll stay on the toothpicks. Slice tofu in half lengthwise through the center, leaving two large flat rectangles. Stack on top of each other, then slice into thirds. Slice again into thirds in the other direction. This will give you 18 bite-sized cubes. If you want smaller bites, slice into fourths.
Mix soy sauce, sesame oil, black pepper, garlic powder and lemon juice, then add tofu. Refrigerate about an hour. Preheat the oven to 350 degrees. Cover baking sheet with aluminum foil and spray with cooking spray. Spread tofu on foil and bake for 20 minutes. Remove, spray top of tofu with more non-stick spray, then flip each piece.
Cover with remaining soy sauce mix, and add a few cracks of pepper, then bake another 15-20 minutes or until firm and starting to get dark and crispy around the edges. While tofu is in oven, mix together mayonnaise and chili powder for dipping sauce. Chill until ready to serve. When tofu is done, serve 1-2 per toothpick.