Preheat the oven to 400°F.
Trim the artichokes by cutting off the stems and tops with a knife. Snip the tips of the side leaves with scissors. Rub all the cut surfaces with cut lemon halves. Squeeze the lemons into a large pot, add the juiced lemon halves, and fill the pot halfway with water. Bring to a boil. Add the artichokes to the boiling water and place a small kitchen towel on top; this will keep them submerged. Boil the artichokes until tender, 12-15 minutes, then remove them with tongs and place them upside down on a towel to cool. When they are cool enough to handle, use a teaspoon to scoop out the spiny choke.