One more thought: brioche buns? (Sometimes we see lobster rolls served on brioche split-top rolls.) Being that classic split-top hot dog rolls aren’t available where you are. You might toast the rolls ahead.
Also you might consider placing the lobster atop a piece of red or green leaf lettuce if you are concerned about the roll becoming too soggy.
None of this is original—simply ideas taken from different lobster rolls I’ve had.