Lithium batteries are funny ducks.
They actually get old, due to age, not just use.
NiCds do get memory effects, but its uncommon for normal use. They can benefit from fairly deep discharge from time to time.
They should be used until almost dead and then fully recharged. Stored fully charged in room temp.
NiMH, do not get memory effects, but also last best when fully discharged and then fully recharged.
Storage the same as NiCd.
Lithiums are different. They love being topped off, and last best if not fully discharged. They age from just sitting around.
The best storage for them is about 75% charged in the refrigerator. It helps them keep just like vegetables.
Fully charged causes them to age faster, and completely dead can ruin one in minutes.
Plus, the warmer they are, the faster they age.
NiCds and NiMHs can be rebuilt and often their capacity can be increased. Many times the packs contain cells that are not full.
There is a local battery place that also rebuilds battery packs and the rebuilds usually last longer than original.
They don't touch lithiums.
Lithiums are dangerous. They can catch fire just sitting there. Most battery packs have safeties built in to prevent shorts and overcharges.
I have a couple of Milwaukee 18 volt lithiums for my cordless drill.
I keep them in a little refrigerator in the shop.
When they wear out, I will replace the cells myself. But, I'm an electronics engineer and since they are for my own use I'm not worried about liability.
Some lithiums have built in safeties, and others use a safety built into the pack they are in.
I don't know which system my packs use, so I will have to wait until I tear them down to see what style cells to order.
This outfit sells replacement cells.
Note that some have built in safeties and others don't.
http://www.batteryjunction.com/