All of the (common) lithium chemistries perform better if the SOC is kept in a safe energy band, say roughly between 20% and 90% of capacity. All (common) lithium chemistries also are happiest at in a thermal band roughly between 0C and 70-ish C.
Get too hot, and charge transfer becomes very inefficient. Get even hotter and thermal runaway happens... see: Boeing 787. (In cars with huge, expensive packs, most systems will actively cool the batteries when needed to keep them in a safe regime.)
Get too cold, get above 90% SOC, or both, and the lithium electroplates the battery anode... permanently. As more and more of the anode is plated, the total capacity of the battery falls off. Many management systems will reduce or stop charging in the cold to prevent this damage. (In cars with huge, expensive packs, most systems will actively heat the batteries to keep them above the danger zone.)
Get too far below 20% SOC, and the anode itself starts to dissolve into the electrolytic fluid, kind of the opposite of the plating described above. Those copper ions will redeposit all over the place when the battery warms, making a big mess of things, reducing capacity, and, ultimately, taking out the battery, because copper is conductive, and so the battery begins to short circuit.
So the trick is to keep the battery between freezing and hotter-than-hottub-hot, and between ~20% and ~90% of its nominal charge capacity, always. In that range the lithium reactions are very reversible and should be able to go back and forth many, many times. Each time you wander outside of those zones, irreversible degradation will occur.