If you need a battery backup system, both lead acid and lithium-ion batteries can be effective options. However, it's usually the right decision to install a lithium-ion battery given the many advantages of the technology - longer lifetime, higher efficiencies, and higher energy density. Lithium-ion batteries are usually more valuable than lead-acid options despite higher upfront costs.
One case where lead-acid batteries may be the better decision is in a scenario with an off-grid solar installation that isn't used very frequently. For example, keeping a lead-acid battery on a boat or RV as a backup power source that is only used every month or so is a less expensive option than lithium-ion, and due to the lower usage rate, you'll avoid many of the drawbacks of lead-acid technology, such as their shorter lifespan.