I'm from Los Angeles, I'm probably the furthest point in the US from New England. So most people here haven't even heard of a lobster roll. I just got back from a road trip in New England and I've had the first four lobster rolls in my life. So here are the top four lobster rolls I've ever had (understanding that these are the only four I've had).
1) Red's Eats (Wiscasset, ME)
2) Cindy's (Freeport, ME)
3) The Clam Shack (Kennebunkport, ME)*
4) The Clam Box (Ipswitch, MA)
All of them were cold. The one from Red's Eats and Clam Shack was with butter, the other two with mayo.
Being Los Angeles, we need to "haute cuisine" everything. There's a joker making a lobster roll made with a brioche, for $22, no less. I haven't eaten it, but I hear it's smaller than anything you can find in New England.
*this was served on a round bun, not a hotdog bun, what's up with that?