Darren,
From memory most LCD Screen power supplies are rated around the 5A mark. This would mean that you are pulling approx 60W of power from the battery. Allowing for ineficiencies in the switch mode power supply and the inverter that figure would probably be higher (around 6A). The current output will probably be written on the PSU somewhere.
Now, assuming a fully charged 85Ah battery you would probably get around 10 hours Max viewing time before the inverter shut down on low voltage (this is a bit dependant on the inverter and overall condition of the battery). This is also assuming no other power is being drawn for lights, heat, fridge, toilet etc..
So, basically yes, you can do it although i wouldn't expect to be able to do it every day for a week!
BTW, don't be tempted to put the '12V' battery directly into the LCD TV. Lead Acid batteries can vary in voltage from 12.8V fully charged (nearer 13.8V while on charge) to 11V when starved of power. Your TV MAY be damaged by this fluctuation in voltage unless specifically designed to allow it. You can buy devices that convert the std. car battery voltage range into a stable 12V DC but if you require more than 2.5A or so it can get expensive (compared to 20 quid for a 600W inverter).
Hope this helps!
Giles