How long can lobsters live out of water?

Lobsters have specialized gills that allow them to extract oxygen from air as well as in water. A thin film of water coating the gill surface is necessary for oxygen to be extracted by the gills from the air. Lobsters can survive out of water for a number of days, but must be kept cool and damp. It is only when the gills are damp and cool can lobsters extract enough oxygen to survive a prolonged period out of water. So my best guess would be 4-6 hours without being able to moisten there gills.

My guess would be that your lobsters died due to you putting them in the salt water. the salinity of the sea is roughly 3.5%, not the 6% as stated prior. Keeping them in the fridge for 7 hours is quite long. Before long the lobsters will start secreting a mucus due to their inability to breathe. If you can get your hands on some fresh seaweed, do so. This will prolong the life of the lobsters to around a day, and possibly two.

I catch lobsters and put them in a paper bag and put them in the fridge not the freezer, the freezer is too dry. Lobsters need moisture to stay alive its how they 'breath' as long as the air is moist/humid the lobster can probably live for 2-3. The one I had in the fridge was still living after 2 days and then we cooked him. so it depends on the surrounding air.