DVD player to IMac

Make sure you have this checkbox checked in the Finder's settings:

But as D.I. Johnson pointed out it only shows up when a disc is in the optical drive.

If you've got everything setup correctly and still don't see a disc gve this a try: boot into Safe Mode according to How to use safe mode on your Mac and test to see if the problem persists. Reboot normally and test again.

NOTE 1: Safe Mode boot can take up to 3 - 5 minutes as it's doing the following; 

• Verifies your startup disk and attempts to repair directory issues, if needed

• Loads only required kernel extensions (prevents 3rd party kernel/extensions from loading)

• Prevents Startup Items and Login Items from opening automatically

• Disables user-installed fonts 

• Deletes font caches, kernel cache, and other system cache files

NOTE 2: if you have a wireless keyboard with rechargeable batteries connect it with its charging cable before booting into Safe Mode. This makes it act as a wired keyboard as will insure a successful boot into Safe Mode.

The macOS will not display the empty DVD drive on the desktop as it would an external hdd or ssd. There must be a disc in the drive for the Mac to display the volume on the desktop.

The DVD device should also be connected directly to the Mac rather than through a hub or dock.

If you go to Apple menu () > About This Mac > System Report... does the Mac see the drive if you select the USB or Disc Burning category on the sidebar there?

What do you mean by "cannot get it to recognize"?

Where are you looking for it?

Does it have disk inside?

Does it appear in the System Information app under Disc Burning or USB devices?

It may not show up in Finder, it there is no disk inside, or the disk cannot be read, or the Mac does not understand the disk.

This is a very old DVD drive... 8-10 years (?).

It's possible that the drivers or firmware for this device were never updated to the 64-bit requirement of macOS 10.15 Catalina? Maybe it doesn't require anything the macOS doesn't provide, though.

Has this drive ever worked on that or any Mac running Catalina?

Did you happen to recently upgrade to Catalina.. or did you bring the drive from another Mac that used an earlier version of macOS?

What type of disc is inside the drive when connected to the Mac exactly?

Did it not appear at all in the System Information App?

Can you post a screen shot of the System Information App with Disc Burning opened?

To confirm or rule out the LG optical drive try it with another Mac or computer.

Is it self powered or get its power from the port?

Is it connected but a hub? If so is the hub self powered?