If your vinyl/record player has phono outputs (left + right), connect these straight up to your DVD recorder's left + right audio inputs. Pop in a blank CD-R/RW and allow it to initialise. Then start your vinyl player and press record on the DVD recorder.
This approach should work well, assuming you are happy to have a few seconds of silence at the start of each track as well as any crackling & pops the records may have. If would prefer to restore the audio to some extent, I would strongly recommend using a CD-RW and then rip the recordings to your PC to edit in a software sound editor as Cressida above mentions. If your PC has a dedicated soundcard (not integrated) and you can easily connect your vinyl player up to the PC, it would probably be easier to record directly to the PC, unless you are not interested in editing your recordings.
Finally, if your vinyl player has only a headphones output, you will need a 3.5mm to 2xPhono (RCA) cable to connect this up to your DVD recorder. If your vinyl player has a 6.35mm headphone socket, you will need a 3.5mm to 6.35mm adaptor (usually supplied with a new pair of headphones) or a 6.35mm to 2xPhono cable. As the headphone socket is usually amplified, I would recommend doing a couple of test recordings to ensure the audio level is not too high or low.
From my experience with the LVW-5045, it is also possible to record to CD-R/RW without any TV handy just by relying on the DVD recorder's display. However, just be warned that the display does not show the free-time remaining and it is a little tricky to finalise a CD-R/RW without the TV, unless you memorise the key presses.
See the section "Recording an Audio CD:" on my following for tips on recording an Audio CD just by relying on the display: