Pour water into a large saucepan to a depth of 2-inches. Add 1 1/2 teaspoons pickling spice, salt, and lemon; bring to a boil. Cover, reduce heat, and simmer 10 minutes. Add salmon and shrimp; simmer 7 minutes or until fish flakes easily when tested with a fork and the shrimp are done. Drain fish mixture, discarding cooking liquid and lemon slices. Let cool.
Remove skin and bones from fish; break fish into bite-size pieces. Layer fish, shrimp, and onion rings in a 1-quart jar.
Combine 1 1/2 teaspoons pickling spice, vinegar, vermouth, sugar, capers, peppercorns, and bay leaf in a saucepan; bring to a boil. Reduce heat; simmer 1 minute or until sugar dissolves. Pour over fish mixture in jar. Cover and chill several hours or up to 5 days. Serve with salad greens, crackers, or other vegetables on an antipasto platter.