What is the exact model of that DVD player, and tge TV?
If it has HDMI output, that would be the easiest way to connect to your TV - you'll switch TV inputs between DirectTV and DVD. If there's no HDMI, your TV must have component video, and analog audio inputs. CHeck your TV manual for details.
The DTV box and BD player connect to the TV with HDMI.
Assuming that the DTV box is already on your wifi network you just need to do the same for the BD streamer.
If the BD player is an home theater system you will need to use either HDMI-ARC or the TV audio output to gets sound from the DTV box to the HTS. Check the TV and LG manual how to set that up.