If you get an analogue LCD TV (i.e. one which hasn't got Freeview built in), it will have similar tuner circuitry to your existing TV, so it's likely that it will work with an indoor aerial. However, different makes of TV (or even different models within the same make) have different tuner 'sensitivity', so it's impossible to guarantee that the LG TV will get a good picture.
If you get a digital LCD TV (i.e. one which has Freeview built in), you might be able to get a decent signal through an indoor aerial but many people find that the switch to digital requires them to change to an outdoor aerial. Digital reception requires a better quality signal. (Additionally, many digital transmitters are currently operating on reduced power, in order to avoid interference to analogue transmissions).
Within the next few years, all analogue transmitters will be switched off so, irrespective of whether you use a digital TV or an analogue one with a Freeview box, you'll need to ensure that you've got a good quality digital signal which might well mean having to use an external aerial.
Chris