1. Cook rice according to package instructions. Transfer to a large bowl; set aside. Stir together vinegar, mirin, sugar, and salt in a small saucepan. Bring to a boil. Cook, stirring constantly, until sugar has dissolved. Remove from heat. Pour vinegar mixture over cooked rice. Stir rice mixture until it has cooled slightly.

2. Form rice mixture into 1-inch balls using wet hands. Make an indentation in each ball with your thumb. Fill with a piece each of lobster and avocado. Cover with more rice to seal. Sprinkle with sesame seeds. Transfer to a serving platter. Serve with pickled plums. Rice balls can be refrigerated, covered with plastic wrap, up to 5 hours. Before serving, let rice balls stand until they come to room temperature.