lithium is really tough to recycle. Aluminum is not. Lithium for batteries is an ionized crystal oxide. It doesn't particularly want to be in that form and when it has gone through many charge cycles, it must be refabricated. Resmelting, like with aluminum, won't work, because it's not the nature of the base metal to be an ionized crystal oxide. I don't know the cycle, but there is a reason we aren't mass recycling these batteries--the process is not at all economical.

EDIT: Batteries are recycled now, actually. I guess it is more economical than it used to be. Go read how they do it and guess who environmentally friendly it is :D

https://waareeess.com/lithium-ion-battery-recycling/

"After shredding, a “black mass” is obtained, which needs to be processed to extract essential metals like cobalt and nickel. The black mass typically includes a blend of lithium, manganese, cobalt and nickel present in distinct ratios. This process requires an intensive amount of energy, and it also degrades the value of the extracted components."

separating out these metals is actually effectively re-refining the elemental forms of the metals. Which requires settling ponds and industrial quantities of acids. Metal refining is often super noxious and releases a LOT of nasty gasses. After obtaining the elemental form of the metals, each will need to be re-ionized and alloyed, which also requires a lot of energy for the smelt and fabrication. Additional materials will need to be sourced for the packaging and layering.

EDIT 2: Lithium is already ionized naturally, since it's an alkaline metal like cesium, potassium, sodium etc. The chemistry involved with using it in an alloy is nuts and well beyond me.