I have a Light and Motion Seca 700 with a Lithium Ion battery. It has a multi-chem smart charger. I have heard that some batteries like NiMH have "memory" and should be mostly drained before recharging, while a LiIon battery is not supposed to have "memory." How should I charge the battery to insure a long run time and battery life?
You should fully charge the battery after every use.
Almost all secondary (rechargeable) batteries will benefit from regular, complete charging. The less you discharge a battery, the more total lifetime capacity you will get from it.
That is, If you take the same battery and regularly use 25% of it's capacity then charge it, you will get C Wh of capacity out of it over its lifetime. If you do the same, but use 95% of its capacity, you may find you only get 0.5C Wh over its lifetime.
Regarding Lithium batteries generally, it is extremely important to use the correct charger for the battery, or the correct mode on a multi-chemistry charger. Otherwise there may be a fire...