Pour the olive and canola oils into a Dutch oven, stock pot, or other wide, deep pot. You should have a pool of oil that's at least 8 inches (20 cm) deep. If not, add more to bring it to that depth. Place the pot over medium heat until the oil measures 275°F (135°C) on an instant-read or candy thermometer. You want to maintain that temperature at a steady rate for at least a few minutes before you proceed.
While the oil is heating, in a wide, shallow bowl, combine the flour, cornstarch, sugar, cayenne, and 2 teaspoons each of salt and pepper. Dredge the lemon slices and the seafood in the flour mixture, shaking off any excess flour.
Line a baking sheet or platter with paper towels or a brown paper bag.
Using tongs or a slotted spoon, gently lower some of the dredged lemon slices into the hot oil, working with just 4 to 6 pieces at a time so as not to crowd the pot. The oil should bubble and sizzle but not spatter.
Cook until golden brown and crisp, about 5 minutes. (Keep an eye on the oil temperature. It will drop immediately after the ingredients are added and slowly climb as they are cooking. Do not let the oil temperature climb above 280°F [138°C].)
Using tongs or a slotted spoon, transfer the lemons to the baking sheet or platter. Season with salt and pepper while still hot. Repeat with the seafood, excluding the squid.
Increase the temperature of the oil to 325°F (163°C) and repeat with the squid. Serve the fritto misto family-style on a platter or a newspaper-clad table along with the fried lemon wedges on the side for squeezing.