The very name of this battery, "lead-acid," is itself a direct clue to its composition, it's built from lead-based plates paired with an acidic electrolyte.
Among common acids, dilute sulphuric acid is the one that reacts reversibly with lead and lead dioxide plates, forming lead sulphate on discharge and reverting back on charging, exactly the reversible reaction a rechargeable battery needs.
Alkaline substances like caustic potash belong to a completely different battery family (nickel-based alkaline cells), while acids such as nitric or hydrochloric acid would corrode the plates rather than support a clean, reversible reaction.
So the correct answer is sulphuric acid.