Welcome to CDFreaks
Sorry for the late reply - just back from holidays.
As far as I’m aware of, the Lite-On models capable of recording to CD-R/RW and CD-RW are capable of recording live audio to CD-R as an Audio CD. If you are interested in a certain model or other features, have a check through the specifications. If it does not list CD-R or CD-RW as media it can record to, then this model does not support Audio CD recording.
From what I recall, the LVW-500x series and definitely the LVW-5045 can all record Audio CDs. One nice feature is the ability to record using standard CD-R’s and CD-RW’s, unlike other standalones that require the more expensive Audio specific CD-R/RW’s. The recorder is very straight forward to use: When a blank CD-R or CD-RW is loaded, the recorder gives a choice of the type of disc to prepare it as. Simply select ‘Audio CD’. Then connect up the phono (RCA) left & right leads to the front or rear input, select the appropriate input source and then press ‘Record’. A new track can be started by pressing ‘Edit’ during the recording. Once the recording is stopped, the next recording will start as a new track. As with recording to DVD or Video CD, the disc must be finalised before it can be played elsewhere.
On most (if not all) the Lite-On models with Audio-CD recording support, you should be able to record without the use of a TV, as the track # and recording time are both shown on the Internal display. Just be warned that the remaining disc time is only shown on-screen (TV required). The only thing you will need to write down or learn is the sequence of keys to initialise the disc (to select ‘Audio CD’) and to finalise the disc.
Unfortunately, it is not possible to record Audio only to the hard drive or record audio in a compressed format (such as MP3, WMA, etc.) However, if you record audio to CD-RW, you can transfer the recorded tracks to the hard drive, erase the CD-RW and reuse it. Then later on, copy the tracks from the hard drive back to CD-R or CD-RW.