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There are a few DVD recorders that I have encountered, which support the recording of Audio CDs. I do know that the LiteOn series has the ability to record directly to CD, however the LG model that you mention only records to DVD and there is even no mention of whether it can record live audio-only content to its hard drive.
My LiteOn LVW-5045 has the ability to record live audio directly to CD. As it automatically initialises the disc and shows the track & time information on its internal display, it is possible to use it independent of the TV, like a Hi-Fi separate but without the requirement of dedicated Audio CD-Râ€™s. Unfortunately, the LiteOn is not capable of recording live audio-only content to its hard drive, however if you use a CD-RW it is possible to copy the disc to its hard drive, blank the CD-RW & reuse it, as well as transfer audio tracks back to CD (as an Audio CD) later on. See the lower half of this page of my review on the LiteOn LVW-5045 to see how this works.
If you do come across other DVD recorders that support the recording of Audio CDâ€™s, it would be worth checking if you can use ordinary CD-Râ€™s or if it requires Audio-specific CD-Râ€™s, since from what I recall, standalone CD-Audio recorders are suppose to refuse regular CD-Râ€™s. Audio CD-Râ€™s have an extra royalty charge on them, which is also why these discs cost more than regular CD-Râ€™s.