Rinse swordfish, drain, and cut into 1-inch chunks. Cut 1 lemon in half lengthwise, then cut halves crosswise into 1/4-inch slices. Discard seeds. Cut remaining lemon into wedges.
Thread swordfish onto metal skewers (10 to 12 in.), separating each piece alternately with a lemon slice then a bay leaf half.
Brush skewered foods with butter and sprinkle lightly with salt.
Prepare barbecue for direct heat.
If using charcoal briquets, cover firegrate with a single, solid layer of ignited coals; let them burn down to desired heat. Set grill in place and measure heat.
If using a gas barbecue, turn all burners to high and close lid for 10 minutes. Adjust burners to desired heat. Set grill in place and measure heat.
When grill is hot (you can hold your hand at grill level only 2 to 3 seconds), lay fish on barbecue. Turn fish as needed, until opaque but still moist-looking in center of thickest part (cut to test), about 8 minutes.
Push foods from skewers and add salt and juice from lemon wedges to taste.