They do require a bit more care then Ni-Mh batteries, but they are an easy and very effective upgrade to any electric gun.
A 7.4v lipo wont increase your rate of fire over a 9.6v Ni-Mh, but it will make trigger response much faster and they don't require any internal gun upgrades to use (unlike 11.1v). They also have the benefit of having a higher capacity for the size of battery.
The downside is that you need a smart charger suitable for LiPo's, a good one can be found for about £35. You also need to do a little bit of reading beforehand to make sure you understand how to safely use them as an improperly charged battery can explode/catch fire, but as long as you charge it properly and don't puncture the battery, they're safe as anything.
In regards to running them flat, if you get a decent capacity I very much doubt you'll ever run in to this. I use a 7.4v 2200mah mini type lipo in my FN2000 and after a full day it's never got anywhere near dangerously low levels.
Edit: You may want to consider changing battery connectors at the same time if you're using tamiya types, it's not really necessary but either Deans or XT60's can handle a higher current and may provide a very small performance increase.