To keep lobsters alive during shipping there are two things that are required; they must remain cool and moist. Lobster deaths during shipping are most commonly caused by oxygen deprivation. The cooler a lobster is, the less oxygen it uses. The gills on a lobster must remain moist to work properly. Be sure not do submerge them, a lobster in fresh water that is too cold can swell up and burst. If handled properly a hard-shelled lobster can live out of the water for up to five days.
Create the right temperature environment for shipping. Optimally you will want to start with lobsters that have been stored at 45 to 50 degrees F. Your shipping temperature should be around the 32 to 40 degrees F. Too much of a temperature change can stress the lobster out and kill it. Be sure to regulate and control the temperature constantly. A lobster will freeze at the same temperature that saltwater freezes, 29 degrees F.
Resist the temptation to feed the lobsters. They should not be fed even two days before shipping them. A full stomach consumes more oxygen.
Pack the lobsters tight enough that they will not get damaged during shipping, but not too tightly. If they are crammed to close together they will deplete their oxygen quickly and there will be an excessive carbon dioxide buildup that will kill the lobsters. Almost any watertight container will do. The size depends on the number of lobsters you are shipping.