If it is fully oooked you can hold it sealed in the refrigerator,and that's probably preferred. And at the same time you can use the heads and shells to make a fast lobster stock. Bay leaf, carrot, onion, Old Bay seasoning. Doesn't need much more than that. You can freeze the stock or use it right away.

I can't say which way is better, but I can tell you that I also steamed lobsters for lobster rolls last summer, shucked the meat and stored it overnight in an airtight container - and it was perfectly fine. (Had no time for shelling the morning of the lunch.) I waited to mix it up with the mayo, etc. shortly before serving.

And now I'm SO craving a lobster roll!