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Unfortunately, according to Peukert Law, when these types of batteries are discharge fast, they provide much less energy. As an example, a typical 80 Amp-hour battery is rated at 20-hour rate. That means only 4 Amps X 20 hours.
However, if that same battery is forced to operate at say 80 Amps, it will not be able to run for an hour to make the same 80 Amp-hours. The actual battery capacity at these high-amp rates is much less.
Short of having lithium batteries that handle high currents better, the best approach with lead-based batteries to supply high power is having more battery bank capacity.
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