Preheat Grill
In a dutch oven (or large pot with lid), fill with water and boil. It's best to steam them first before grilling.
Carefully cut 1/2 inch off the tops of each artichoke (pointed ends) and thrown into pot with 1 lemon cut in half. If you want a pretty presentation, take kitchen shears and snip away all the pointy tips of the leaves (optional).
Boil with lid for 15 minutes.
Remove from water on a plate and cut the artichokes straight down the center through the stems.
Brush on olive oil, minced garlic, lemon juice of 1 lemon, and salt on all 4 halves.
Place artichoke halves cut side down on the grill for 5-10 minutes. You want markings so try not to move them around.