One nice feature with the AllWrite Lite-On's is that they do not require Audio specific CD-R's or CD-RW's, unlike most dedicated standalone CD recorders that will not accept regular CD-R's or CD-RWs. Recordings carried out to CD-R/RW are written as standard CD-Audio and will playback in any CD player capable of playing recordable discs. I can confirm this with my LVW-5045 as I played back a CD-R disc recorded in it on a CD Hi-Fi system that we bought back in 1991 and also in a portable CD player.

On the Lite-On models with a display, such as the LVW-5045, the front-display is enough to see the recording progress and current track number, without the need to hook up a TV. However, a menu navigation is required to finalise the disc, although this can be done by learning which key sequence to press to finalise the disc without a TV to see the menus. I'm not sure what other brands are capable of writing CD-Audio.

On the other hand, if you are just looking to record audio, but don't care about demultiplexing the audio from blank video tracks later, I would go with CDan's suggestion and record in long play or extended long play to DVD, as pretty much every DVD recorder would be capable of recording audio without the video input connected.