In a medium bowl, beat cheese with lemon juice, herbs, and pepper; stir in crab.
Break tough ends off asparagus. Blanch in 1 inch of boiling water in a large skillet with a lid, or steam standing upright in a couple of inches of water in a tall, narrow pot, until crisp-tender, 2 to 5 minutes, depending on thickness of stems. Plunge into an ice-water bath for 1 minute; then pat dry. Trim asparagus to abut 5 inches; from the trimmings, cut as many 1/4-inch rounds as you have tulip petals. Save extra ends for salads.
Fill each tulip petal with about 1/2 a rounded teaspoon of crab mixture and garnish with an asparagus round. (If your petals are large and asparagus thin, you can use 3 rounds to garnish each filled petal.) Arrange asparagus in a fan on a serving platter and place tulip petals alternately (or create your own pattern).