Mixed with lemon juice and pepper, the frozen watermelon puree is a delicious riff on a classic mignonette.
Puree watermelon in a blender until smooth. Strain mixture through a fine sieve into a 5-by-9-inch nonreactive loaf pan; discard solids. Stir in lemon juice, 1/8 teaspoon salt, and 1/2 teaspoon pepper. Cover with plastic wrap; freeze until firm, about 3 hours.
Scrape granita with a fork until fluffy. Freeze again while shucking oysters.
Shuck oysters, and arrange on a bed of crushed ice. Garnish ice with lemon zest. Top each oyster with 1 to 2 teaspoons granita toward the narrow end of the oyster shell.
Granita can be frozen for up to 1 week. Rescrape before using.