lipo's are VERY user-friendly ..
but have to be charged with lipo-specific-settings so you need a charger that has a lipo-function.
Secondly it is important that the tension on a Lipo-battery does not go below 2,9V per cel (or 3,0 or 3,3 V to be on the safe side).
Per cel, that means that in 1/10th, where we race with 7,4V lipo's, that 6,0 (or 6,6V) is the minimum-tension the battery can have.
Going below this tension, the chemicals inside the cel will change and the battery can become unstable.
A lipo going unstable can go into spontaneous fire, with a VERY hot flame so that it something you would like to prevent if possible

An ESC which is called lipo-compatible wil have a function that shuts the motor or throttle whenever it detects the Lipo-tension to be too low.
So, when the tension drops below 6 or 6,6V, depending on the ESC-settings, the car will stop.
Also, you have to know that generally speaking a lipo gives power until the end. The power-curve is very flat. It is only very near the end that the amps will drop.
Conclusion: a Lipo-compatible ESC is a safe thing to have.
But you can drive a lipo-battery with any normal ESC ... as long as you don't exceed the driving time.
If you notice a drop in performance, you have to stop immediately and recharge the lipo.
This is still not something you have to worry too much about. Modern Lipo's often have a capacity of more then 5000mA. With a 10 brushless motor, or, let's say, an 17T brushed, this will give you driving times of +20 minutes ... so pleeeenty of time.
I recently tested my X11 Predator (1/10th 4WD buggy) with a 10 brushless .. and drove 42 minutes until the lipo-cut-of kicked in.
A lipo-cutoff-device can also be bought as a stand-alone device. I know LRP has them.
hope this helps you