Years ago a mechanic friend of mine intentionally wanted to seize a Datsun engine by running it without oil (a long story). Took over 15 minutes, a lot longer than he expected. As a 16 yr old kid I inadverdently backed my Mom's '70 Mercury wagon off the ramps without oil while doing a lube job, probably about 20 seconds or so. No obvious harm at all. And through cumulative dry starts over an engine's life, it essentially runs many minutes without oil.
A deep cycle battery can provide a surge when needed, but nothing like the surge a car battery can. A deep cycle battery is also designed to be deeply discharged over and over again (something that would ruin a car battery very quickly). To accomplish this, a deep cycle battery uses thicker plates.
When people think about lead batteries, they usually think about a car battery. These are starting batteries. They deliver a short burst of high power to start the engine. There are also Deep Cycle batteries. These are found on boats or campers, where they're used to power accessories like trolling motors, winches or lights.