The Live should have come with an optical cable (the Toslink).
If you are asking whether the speakers connected to your receiver will work when you are watching the TV only (say watching either cable or antenna inputs) you need to connect the TV outputs to your receiver. Hopefully you have audio out somewhere on your TV.
The way to look at it is this – every source (DVD, Live, “television”) needs to go into your receiver for you to hear it over the speakers that are attached to the receiver. So you have to put the audio out of the DVD player into your receiver, you have to put the audio out of the Live into the receiver, and you have to put the audio out of your television channels (which in this case are coming directly from the TV) into the receiver. Then to hear each source your receiver must be set to the appropriate setting for each.
The TV also needs each source to have a video input (just like your receiver needs an audio input). In the case of cable or antenna that comes directly to the TV. The DVD player and the Live can be connected to your TV in a variety of ways (HDMI is the best, then component, then composite). In each case you must choose the video input on your television side (so you choose the audio input on your receiver, and the video input on your TV).
The television usually has built-in speakers and most people who have receivers with separate speakers turn off the internal speakers on their TV (they aren’t needed). There should be a way to do this in your TV (or you can turn the volume of the TV all the way down). This won’t affect the audio output of your TV to the receiver.