Fill a pot with enough water to cover the artichokes and add 1 teaspoon salt in. Bring to a boil, then lower the heat.
Prepare a charcoal or wood fire.
Immerse the artichokes in the pot with the simmering brine. Simmer gently until cooked through and fork-tender, 15 to 20 minutes. Drain the artichokes on paper towels and set aside until cool enough to handle.
When the grill is hot, for small artichokes, open out the leaves and press them onto the grill so that they flatten slightly. Cut larger artichokes into quarters and then grill. When nicely browned, remove them from the grill and season with 0.5 tablespoon lemon juice and 1 teaspoon salt.
Meanwhile, prepare butter sauce; melt butter in skillet over medium heat.
Whisk in remaining lemon juice, lemon zest, salt, and pepper.