Can I charge a lead acid battery with a lithium ion battery?
Yes you could charge a 12V battery with a 15V battery. Since you can not control any parameters when charging this way (arguably you control voltage) it is not optimal, but a constant voltage charger is probably good enough for a lead acid battery but possibly harm your lithium ion battery. With other technologies you probably would like to control the current and possibly the charge cycle.

There are many modes of charging. I include this link after a quick google search where you can read the section "Basic Charging Methods" on this page http://www.mpoweruk.com/chargers.htm.