I did this a few times - the lobsters were on sale air-side at Logan - but haven't done it for 10 years or more.
They used to get packed in little cardboard boxes with two of them to a box, claws all cable-tied together with a little cold gel pack to keep it cool.
On one flight I fished the box out from under the seat upon arrival to find one of them had wandered off during the night....obviously didn't get noticed by anybody on it's travels, but can't imagine it smelt good when it finally expired.