@OP for those not in the know it is easy to confuse two of the major forms of lithium based secondary cells
You get Lithium Ion batteries, and Lithium Iron Phosphate batteries.
Lithium Ion batteries are normally made with the use of polymers, and are known as LiPo batteries. LiPos are common in things like cellphones, tablets and laptops. They have an extremely high energy density, and depending on how they are made they can have very high instantaneous power densities too. The trouble with them is that if they are short circuited (like being impaled by something metal) they tend to catch fire. Not very good for things like an electric car in a road accident... but fine for things that don't tend to get impaled like cell phones.
Lithium Iron Phosphate batteries - LiFePO4 - on the other hand have lower power and energy densities than LiPos, but still much better than Lead-acid batteries (including gel/membrane types). LiFePO4s are used quite extensively for things like electric cars, since they have quite a broad DoD to cycle life ratio, they can charge and discharge relatively quickly (much quicker than Lead-acid) and they also tend not to catch fire nearly as easily as LiPos.
kWh for kWh of storage, LiFePO4 are more expensive than Lead-acid, but only just. On the upside, you can charge and discharge LiFePO4s much quicker than a lead-acid battery of the same kWh - it makes them more attractive for things like buffering renewable energy to be used later to make 220V AC electricity (charge LiFePO4s during the day with solar PV panels, use the batteries at night).