Most 115VAC plugs in cars and trucks only provide a few hundred Watts of power (perhaps, around 2-5 amps) for small accessories, like phone chargers, DVD players, etc. This outlet will NOT power your Airstream's air conditioner, which needs over 15 (probably around 16-20) amps of 115VAC. To run an air conditioner, you will need one or more RV generators.
If the weather is mild and (day/night) temperatures are around 86/65 degrees, you might be able to get by with only FantasticFans; especially, since you will probably be out enjoying the music festival during the heat of the day. However, if record high temperatures are encountered, you may be very uncomfortable during the day. Note: The air conditioner runs off of 115VAC, and it is not connected to the 12VDC circuit (i.e., the batteries) in your Airstream.
Regarding charging your trailer batteries using the 115VAC accessory plug in your Lexus (and a 115VAC battery charger), this will not work. While this is possible in theory, you will overload and possibly damage the inverter in your Lexus. At the very least, you will probably burn out the fuse or pop the circuit breaker.
You can charge your Airstream's batteries using the trailer umbilical; but your TV's alternator is designed only to top-off a very slightly discharged automotive battery, not two, heavily-discharged, deep-cycle marine/RV batteries. Recharging your Airstream batteries using your Lexus will take many hours every day, if you use a lot of 12VDC power at night. However, if you limit your 12VDC, you may be able to stretch the batteries for several days without recharging. Note: Heavy use of FantasticFans will probably require daily recharging.
You may wish to check on renting a generator (or two) for a few days. We looked at Honda EU2000i's at a rental shop before we purchased two (one standard, and one companion). However, summer temperatures in the desert southwest are much higher than in Ohio.