Why do we use a lithium ion solar battery for storage?

There is no such thing as a “lithium ion solar battery”. Li-ion batteries can be use to store electrical energy from ANYTHING, NOT just solar.

Secondly, li-ion battery is not the only way to store solar energy. Molten salt, compress air, pump hydroelectric are all various forms of solar energy storage. And just like how Li-ion batteries can store energy from anything, these forms of storage can also store energy from anything not just solar.