It depends somewhat on the fuse size for the lighter circuit. Let's say its 10 amps on a 12 V system. The maximum steady DC power to the lighter is then 120 W. If the inverter is 95% efficient you could expect to run about 114 W of of it without blowing the fuse.

Be careful about just bumping up the fuse in the lighter circuit as its wiring may not be rated for that steady current. The worst thing that could happen then is a fire which is plenty bad ...............

My 750W inverter cables directly to the battery and has somewhat healthy DC leads ...........

Good Luck, Kitz