Just did very approximate calculations; with 10g of lithium per drone*, and assuming the Russian and Ukrainian drone efforts consume 5m units a year**, that'd be ~50 tons of lithium deposited into the environment per year, mostly within, let's say, 50km of the grey zone***. It's only about $20,000 / ton****, which means $1m of metal*****.
So to answer my own silly question: no, it won't be economically viable to scalp the top few inches of topsoil and extract the lithium from it.
* Roughly right for quadcopters / small FPV; larger and longer range ones will have more, so this is a bottom bound. (OTOH longer range UAVs will tend to use ICE kerosene rather than batteries
** Changing all the time as both sides try expanding production as fast as they can manage. Ua are scaling much faster at time of writing
*** Handwaving. Contact zone's hardly moved since early 2023; OTOH Ua are pushing range limits on small battery-powered form factor, saw a 60km claim for the Logistics Lockdown operation the other day
**** There was a big spike to the $70-8000 range in 2022; median price is closer to $10k than $20k
***** (IDK the chemistry but presumably it's in an exciting range of different compounds, depending on how many bits the battery was blown into, how hot / pressured the blast wave was a few tens of mm from the boom, what other stuff was in the vicinity that the lithium would combine with, etc etc.