You're right, there's a lot of confusion with regard to maintaining batteries since the procedures are different for different chemicals. A lot of technical support manuals and personnel offer plain wrong advice.
The authoritative advice with regard to using and maintaining a Li-ion battery (all T40 batteries are Li-ion) is:
Avoid discharging the battery to below about 10%. Especially avoid completely discharging the battery. Also avoid leaving it in discharged condition for prolonged periods of time. 3/4 to full charge is the optimal charge bracket for Li-ion battery longevity. This means whenever you use the battery, make the cycle as shallow as possible. This is in direct conflict with the notion of long battery life, which means that you shouldn't pay too much attention to these guidelines and just use the battery as you need. The battery is rated for about 300 full cycles, and it can withstand perhaps 4 times that if you only half-cycle it (i.e. 1000 or more 100%->50%->100% cycles). No special maintenance procedures (like deep cycle) are applicable to Li-ion batteries.