The CAA have an interesting article -
Dealing With In-Flight Lithium Battery Fires In Portable Electronic Devices (478 KB PDF). They used a blow torch for ignition!
The good news is that normal fire extinguishing equipment (including fire blankets) will put out the fire, the bad news is that it could do severe damage to the pax whose laptop caught fire.
It seems as though special precautions are needed for bulk carriage of Lithium cells, but individual items are allowed (otherwise, you'd be banning every video camera, laptop and mobile phone manufactured in the last few years).