Fill a large bowl halfway with water. Squeeze the lemon halves into the water and add the lemons. Trim the stem of 1 artichoke. Starting at the base, bend the tough outer leaves back and pull off where they break naturally. Using a vegetable peeler, peel the dark green skin from the base. Halve the artichoke lengthwise and scoop out any choke. Add to the lemon water. Repeat with the remaining artichokes.
Heat the oil in a heavy large saucepan over medium heat until a thermometer registers 350 degrees F. Drain the artichokes and pat dry. Working in 2 batches, add the artichokes to the hot oil and cook until they are tender and golden brown, about 8 to 10 minutes. Using a slotted spoon or tongs, transfer the fried artichokes to a paper towel-lined plate to drain. Sprinkle with salt while artichokes are still warm and serve.