Grilled Swordfish with Lemon and Caper Sauce

unsalted butter

large lemon, peeled, cut crosswise into 8 1/4\" slices, seeded, with all the juice

drained nonpareil capers

Sea salt and freshly ground white pepper

swordfish steaks cut 1 1/4-inch thick (about 1 pound each)

(very green) extra-virgin olive oil

finely chopped parsley for garnish