150Watts is good to go for a laptop. I did it for a 5000mile camping roadtrip out west last spring and had the same concern. You dont want to use that inverter for anything but a laptop, a battery charger, or similar small device.
Yes, the cig lighter has a fuse on it, but if you actually look at the wire to the lighter it is ungodly thin. I forget the gage, but it heats up if you push her. Typical for foreign cars I've found. So just a word of caution, but I really wouldn't worry. Though, I would never even think of running a 400Watt inverter off the cig lighter as stated above. That is downright dangerous, and you even run the risk of messing your ignition relays.
I ran a tap off the fuse panel for an additional plug (because I had multiple small devices running) and with a thicker wire and noticed it didn't get warm. Note this would give you the option of running something to the trunk or back seat if you needed it and know how to use the correct gage. (longer the run the thicker required).
Probably doesnt apply to you, but if you need to run anything big you need a bigger inverter wired directly to the battery and be cautious to not drain it.