Fill a 1-quart bowl with water and squeeze the juice of the lemon into it.
Remove the tough outer leaves of one artichoke to expose the more tender leaves within and then, using kitchen shears or a paring knife, cut off the top half of each leaf. Trim the base and peel the stem, then scoop out the hairy choke in the center of the artichoke with a sharp spoon (if possible) and discard. Once all the cutting and trimming is done, the artichoke should look like a rosebud. Place the artichoke in the lemon water. Repeat with the remaining artichokes.
When all the artichokes are trimmed, drain and pat dry. One at a time, put the artichokes on a clean work surface and press down on them gently to force the leaves to open; alternatively, use your fingers to spread out the leaves.
In a medium saucepan, heat the olive oil over medium heat until it reaches 300°F on a deep-fry thermometer. You can check the oil temperature by dipping the handle of a wooden spoon in it — when the oil is ready, it will gently sizzle and bubble up around it. Drop a couple of artichokes at a time into the hot oil and press them down with a fork or with tongs. Cook for 5 to 10 minutes, depending on the size.
Transfer the half-cooked artichokes to a plate lined with paper towels to drain and repeat with the remaining artichokes. Using a fork or your fingers, try to separate the leaves of the artichokes so they open up like a flower.
Raise the heat and bring the oil to 350°F to fully fry and crisp up the artichokes.
Fry the artichokes one at a time: add the artichoke stem side up to the hot oil and cook for 3 to 4 minutes, then flip it with kitchen tongs and fry until the leaves brown, pressing the artichoke gently down into the oil so that it opens up like a flower. Transfer to a plate lined with paper towels to drain.
Once the artichokes have cooled slightly, sprinkle them with salt and pepper. Serve immediately, with a few slices of lemon on the side, if desired.