Your Luxman is a classic high power stereo receiver. As such, it was not designed to do any of the audio/video switching that modern HT receivers can handle. That said, you can still use it to vastly improve the sound in your new HDTV/blu-ray system.
It is generally accepted that the built in speakers in TV's, even HDTV's are generally very inferior to decent stereo or 5.1/7.1 speakers. Unless your proposed LG HDTV has a built in "sound bar", the internal speakers are stereo anyway.
For years I fed the stereo output of my primary TV into a stereo receiver via the simple red/white RCA audio cables - the resulting sound on decent stereo speakers with ample low frequency reproduction was vastly superior to the TV's tiny cheap speakers. In my den, my little 32" LCD HDTV and satellite TV box is still connected to a stereo receiver and vintage stereo speakers.
Your cable TV set-top-box will have red/white stereo output connectors, along with Toslink optical digital audio for Dolby Digital 5.1 output. Your Luxman will not be able to use the Toslink, but it can certainly use the red/white analog stereo audio outputs to feed the sound into an auxillary input on your receiver. Once you have done this, a simple listening test to a movie playing on the TV will convince you the sound on your stereo system is much, much improved over what the built-in speakers on the TV can provide.
I'm getting a little long-winded here, but another option "MAY" be to connect your cable box and your blu-ray DVD player to the TV via HDMI cables, then use the audio out connectors usually provided on the HDTV to feed your receiver's AUX input. That way, both the TV's speakers will work, when you don't want to turn on the stereo system, and you can switch on the stereo system when you want more dramatic sound with your TV viewing. The reason I said "MAY", is that every HDTV handles pass-through audio differently. But most will downmix any digital audio coming in on the HDMI input cables to stereo and make it available at female RCA red/white connectors to feed an outside audio system. They also feed this signal out on a Toslink optical and/or digital audio coax connection, but that's not an issue with your receiver.
Give it a try, you can always install a 5.1 system later, if you find you really want one and use your vintage stereo system in another room for music listening. Good luck.