Hello Richard, Conventional TV use a CRT (Cathode Ray tube) and the support systems needed to run the CRT were more tolerant of fluctuating voltages than many of the more modern systems. Many of the LCD type screens need a lot of computer type processing chips to produce the signal matrix to drive the screen. These are usually very sensitive to the correct voltage, and even as little as 0.1V (100mV) difference can cause them to malfunction.
Although cars are said to have a 12Vdc system, in practice it can easily vary between 10 and 14.5 V, depending on what is running, and whether the alternator is charging. As you can see this is quite a wide range, and without further supply line regulation there is a strong possibility that your LCD TV may not work properly or at worst be damaged. If the TV has been designed to work in cars, then it should be protected from these variations, but if it is designed for domestic use with its own power supply to convert 230 to 12V, then you must use more caution.
You can get special switch mode power supplies designed to work in cars that produced a stable 12V dc output (see your local Maplin electronic shop or online catalogue). Or you can use Les' solution of a 12V dc to 230V ac inverter and your tv's plug in power supply to reconvert 230 ac to 12V dc.