Hello Alan, and others
You have some answers above, that seem to contradict each other, and there are elements of truth in all, so I think you may need a bit more explanation. I hope this does not confuse you further.
As you mention 12V power lets consider that first. The "12V" system in a caravan is usually anything but 12V.. when the charger is on the voltage can rise to 13.8V, and when the battery is running down the voltage will fall ultimately to 0V, but in practice a minimum of 10V to 10.5V would be considered a flat battery.
Another factor that also affects the voltage available to the TV, is the total Amps being used by all the appliances which will cause a 'Voltage drop' along the wiring between the battery ad the TV. The more Amps used the greater the voltage drops.
This wide range of voltage can be a problem to some makes of LCD television. Some sets require 12V exactly; others can tolerate a wider range of input voltage. Most sets have a power pack, which you use at home that converts 230V ac to the accurate 12Vdc the set needs.
There is another way that you might resolve this issue, and "John" has alluded to it. There is a device called an 'Inverter' which connects to a 12V dc supply and produces 230V ac (like mains supply). It is the converse of a 12V power supply.
Whilst it is not entirely accurate because of inefficiencies we can for the purposes of this discussion assume that both power supplies and inverters are 100% efficient. This means that Power In (Watts) =Power Out (Watts). In electrical terms power (Watts) can be calculated from Volts and current (Amps):-
Volts X Amps = Watts
If your LCD is rated at 12V at 5A then using the above formula we can see the power rating is 12V x 5A = 60W. At 5A current, a significant voltage drop may be caused in the wiring. Because Power (Watts) is conserved through the power supply then if the input voltage is now 230V then current is given by translating the formula so that Volts DIVIDED by Watts = Current : 230/60= 0.25A (Approx)
This much-reduced current will produce a much smaller voltage drop in the cable,
Incidentally this is why the generating companies distribute power along our pylons at 11,000V or even 230,000V to reduce transmission losses due to cable resistance.
Inverters have limited power capacity (Watts). These will be fine for the TV, but don't expect to run high-powered equipment such as a hair dryer or microwave from them. The sets own power supply can be plugged into the inverter. It does mean you can use some other low powered equipment as well such as a DVD player or a laptop computer. But be warned that they will use up battery power quite quickly at. There are power losses due to inefficiencies these will be about 10% and are usually lost as heat.
Sadly I cannot offer any guidance on the suitability of different models, so it is important to tell you TV supplier of your intended usage, and to ask for a written guarantee that the product will work under such wide operational conditions: then if it does not, the retailer has failed to supply goods fit for purpose, and you would be entitled to your money back.