Yes traditionally the lobster rolls and lobster meat is served to you cold and not warm.
Lobster rolls are typically served cold with mayonnaise either tossed with the meat or spread onto the meat for the lobster roll.
If you prefer to have the lobster meat warm or hot when served you certainly can have it that way and just let the waiter know or if you're making the lobster roll yourself just serve it warm.
I prefer the lobster meat to be warm myself so I always ask to be served the lobster roll warm and the waiter lets the cook know about it and they serve it to me that way.
I tried lobster rolls cold before and they just aren't as good to me that way but a lot of people to enjoy the lobster rolls cold.