How much current can lead acid batteries safely supply?
Lead acid batteries are fantastic at providing a lot of power for a short period of time. In the automotive world, this is referred to as Cold Cranking Amps. From GNB Systems FAQ page (found via a Google search):


  Cranking amps are the numbers of amperes a lead-acid battery at 32 degrees F (0 degrees C) can deliver for 30 seconds and maintain at least 1.2 volts per cell (7.2 volts for a 12 volt battery).


A car actually doesn't need 30 seconds, normally only a few seconds to start, except in very cold weather or other extreme situations. But 30 seconds means you could give it a few tries before the battery (if it started charged and in good shape) becomes a problem.

Picking one battery at random from Sears DieHard, I found 730 CCA. That's 730 Amps at 12 V. That is a LOT of power.

The end result is that you have to find the right battery combination of:


Max. surge current or CCA
Total capacity, typically in Amp-hours
Size &amp; weight
Cost


An 18 V lead-acid battery could be a tiny little thing. Or it could be like a typical car battery, only 18 V instead of 12 V.

If you are looking at a one-off or small production run you may be better off leveraging car battery technology - mature, inexpensive, easy to replace - rather than 18 V or something else more unusual. But that only works if the size &amp; weight parameters work for your particular project.