What is the max watt that the cigarette lighter supply?

If it's like our 2018 that should top out at 10 amps / 120 watts. That's a very common rating for lighter plugs.

 

If you still have the owners manual, find the fuse for it and do the math.

P.S. In your profile, it says you have a 2012 model.

 

I believe the 1. 7 amps Max is the charging current and not the operating current (if the battery was fully charged). If you have one of those kilowatt meters, it's easy to see the draw running off your AC adapter in your home.

If you're handy with a voltmeter, you could also measure the amperage from an inline reading, but I wouldn't recommend that for the novice. It is potentially dangerous.

 

Get a 100-120 watt inverter and try it. The worst that is going to happen is that you burn out a fuse. Lots of people use laptops successfully on small inverters powered by lighter plugs. The output on the laptop supply is marked 65W, so that's either a small or modern laptop or both. Even with crummy efficiency on the part of the power brick, that is unlikely to ever draw more than 90W. Allow a little for another stage of inefficiency at the inverter and you may come close to the limit but I think you'll be fine.

 

65 watts is about 5.4 amps at 12 V.
Very likely that the "cigarette lighter" plug will be OK with that.

Why don't you just get a new battery ??
Might be cheaper.....and certainly more useful......than the inverter.

 

If you don't wanna go the new battery route, I think it might be more economical to buy a 12v(auto) adapter for your laptop. It dodges the odd math and has way less power loss. It's awkward from a power efficiency and conversion standpoint to take DC power, convert to AC power, then back to DC power.

 

I run a 400 watt inverter from my 2013 Prius C cig lighter. It charges two cell phones via usb and two 110v outlets. One is my laptop and the other is a medical camera. No problems.