First, to ensure freshness, all live lobsters should be shipped overnight. Two things are important - cool temperature and moisture.

To keep lobsters alive during shipping make sure that they remain cool and moist. Lobsters usually die in shipping due to lack of oxygen or poor handling by the shipper.

Keep them moist (but not submerged in water) because their gills need moisture to function. 

Keep them cool. Your lobsters should be cooled before they are packed. If possible, start with lobsters that have been kept at a temperature of about 45 to 50 degrees F. The best shipping temperature is between 32° and 40 degrees F. Lobsters will freeze - so be careful. Also, don't use dry ice for packing - they could freeze or suffocate - dry ice is, after all, carbon dioxide, and will deprive them of oxygen. One good shipping combination is to wrap the live lobsters in fresh seaweed and cool them with 'freezer packs'.

Here are the keys to success:

First, start with fresh, lively, firm shelled lobsters.
Second, keep them moist - damp fresh seaweed is good. It pads and protects them, and it keeps them moist. Don't submerge them in either fresh or salt water.
Third, keep them cool - freezer packs are good. Don't use dry ice.