Stir together first 4 ingredients in a medium bowl; gently stir in lobster. Cover and chill until ready to serve.
Melt 1 tablespoon butter in a large skillet over medium heat. Add half of buns, cut sides down, and cook 1 to 2 minutes or until toasted. Repeat with remaining butter and buns.
Arrange arugula on rolls, and top with lobster mixture and bacon.
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