In this case the electrode is metallic lead and the electrolyte is water containing sulfuric acid.
The electrode-electrolyte "interphase" is a solid coating based on lead sulfate, that forms on the lead plates after extended recharge cycles. This doesn't redissolve very well during use after a while when the electrolyte has become oversaturated with lead ions, and the electrodes have been "replated" so many times. Especially when recharged from near-death.
One antique way of restoration without disassembly was to agitate the battery using an industrial vibrator to loosen up the solids, then dump out the (highly toxic lead-containing) electrolyte to physically remove as much sludge as possible. Followed by repeated filling using distilled water, agitation, and dumping until the waste water looks OK. One final fill with DI water (which acts as a very weak electrolyte at this point) and a reverse charge until an amp or two has been reached for a bit, to deplate as much oxidized coating as possible into a virgin solvent.
More agitation, dumping, rinsing, and finally replace with fresh acid.
Desperate measures for desperate times, not too economical today unless similar wastewater is already being handled in a scale that dwarfs a single battery, and fresh acid is obtained surplus or purchased at bulk pricing as well.
Restoring the functioning of the original electrodes in situ is a bit of a different ordeal. But they're working on it :)
If they were easier to reuse like that and it was done more often then disposal for that lead saturated acid would likely be more available.
Good rundown of the process here: https://batterycouncil.org/battery-facts-and-applications/ho...