I assume you’re referring to starter motor batteries for ICE cars.
Lead acid is just more robust than lithium batteries.
It can handle many fault conditions, even short circuit without catching fire. Overcharging to some extent isn’t an issue either.
They can handle a great deal more charge cycles than lithium based cells and they are not damaged irreparably by a deep discharge.
On the negative side they do produce hydrogen while being charged which needs to be vented safely and they are a lot heavier and larger for their capacity.
Ignoring the economies of scale already present in the supply chain, lithium would not necessarily cost more at current prices especially considering the cost savings from not shipping lead around. However the automotive companies know that if they switched to lithium the price would go through the roof due to supply issues. There just isn’t enough supply in the world to cover all the starter batteries being made right now, which is a lot more than EV batteries.