Lithium batteries make great starter batteries because they are capable of much higher discharge rates than lead acid batteries for a given amount of energy stored. This one of the factors that enables users to install a much lighter lithium battery than the lead acid equivalent - a 10AH lithium battery might have the same cranking performance as a 20AH lead acid battery.
Lithium batteries also have other characteristics that need to be understood and accounted for in the electrical design. For example, where a lead acid battery has a fairly smooth discharge curve (in that the output voltage decreases somewhat linearly as the battery discharges), the discharge curve for the typical lithium battery has a very sharp drop off once it discharges beyond a certain point. One minute it'll be delivering enough voltage and the next it won't. This, combined with the smaller amp hours rating for a given cranking performance (a lithium battery capable of cranking say an O-200 will have less amp hours than a lead acid battery capable of cranking the same engine), makes a lithium battery quite a different proposition as a backup battery. A further consideration is that lithium batteries are damaged by both over-voltage and under-voltage. A couple of incidents will illustrate. A friend of mine installed a lithium battery in his Zenith CH200. One day when he went to fly he found the master had been left on and the battery was flat. He checked the aircraft throroughly and then hand propped it. He confirmed everything was normal, the alternator was charging and then took off. 15 minutes later (at 4,500ft) the cabin filled with acrid fumes. He was able to get the canopy open and perform a forced landing in a field. Analysis showed the lithium battery had been damaged by the complete discharge and reacted badly to being recharged. He was lucky. Less fortunate was the pilot of a LSA seaplane where a lithium battery caught fire in flight (less than an hour after it was installed) and melted the epoxy/carbon fibre tailboom. Research into this incident indicates an issue with lithium batteries in electrical systems that use PWM (pulse width modulation) voltage regulators (e.g. most Rotax and automotive installations). When exposed to voltages above about 14.6 volts lithium batteries start to develop little crystals inside that can short circuit the cathode and anode. When enough of these build up the battery will experience a catastrophic failure. Alternators produce something like 22 volts peak. This is rectified and then 'regulated' (in a PWM system) by switching the voltage on and off to produce a waveform that averages the required voltage - usually 13.8V, a suitable voltage for charging a lead acid battery that's nominally 12V. The problem is that while the waveform coming out of the regulator is nominally 13.8V (and averaged over time actually is 13.8V), at any instant in time it could be any voltage in the range from zero to the peak voltage of the alternator (around 22V). Whenever it's over 14.6V it'll be doing damage if there's a lithium battery in the system. Lead acid batteries tolerate this method of regulation. Lithium batteries much less so. The more damage (those little crystals) that accumulates the greater the likelihood of a catastrophic failure. In many cases people have used these batteries with no dramas - I had one in my (Rotax powered) aircraft for 70 hours of incident free flying. But that was before I knew what I know now. Although these batteries are marketed as a drop in replacement for the lead acid batteries that are standard in many recreational vehicles, the differences can be significant - especially in an aircraft. I'd now only use a lithium battery if the charging system can never produce a voltage higher than 14.6V. And if the battery was ever fully discharged (e.g. by leaving the master on) it'd be going in the disposal bin. Cheers, Tony