The issue of loss of capacity with battery charging and discharging is due to crystallization of pure concentrated chemicals inside the battery. Once crystals start to form they do not want to revert back to a liquid state again, and the battery permanently loses some charge/discharge capacity.
This is why sometimes old lead-acid batteries bulge outward when they are failing... huge lead crystals have formed which apply pressure to the lead plates and case and bend them. Growing crystals can also form electrical shorts between plates and ruin the individual cells.
The goal of not discharging too far is to try to stay out of the area where crystallization becomes much easier due to high concentrations of the chemicals in the deeply discharged state.
Lead acid cells should ideally never be allowed to stay discharged very long, and rapid recharge is recommended. Though once charged they need to trickle charge to prevent damage from overcharging.
Lithium cells are generally more tolerant of full charge and discharge cycles. The construction of the cell and the surface features of the plates can help prevent crystal formation. Slow charging generally should not affect the life of lithium cells as much as it can with lead-acid cells.
It's often said that lithium cells have a fixed life of about five years, though my own experience does not bear this out. We have about 15 IBM Thinkpads with original lithium battery packs from a decade ago and they all still hold at least 2 hrs of charge.