The cigarette lighter plug will probably put out enough Amps for your charger (probably good for 20A+), although the "auxiliary" sockets in some vehicles are only fused for ~10A (they're not meant for a cig lighter, just 12VDC accessories). Most vehicles switch the power to the sockets off with the ignition/accessory switch, so you may have to leave your keys in the car to keep the sockets powered up.

As mentioned above, be sure to have a safe surface to put the batteries & charger on in case they overheat, puff, or catch fire. It would be best to have everthing outside the vehicle, on the ground or other safe surface.