MacBook Air M1 not detecting LG monitor via USB-C to HDMI

macOS has become progressively less tolerant of video data packet loss due to sub-par cables. There were several reports of setups that worked in Sequoia not working in Tahoe and likewise in Golden Gate, with nothing changed but macOS. 

One recommendation is to try a new cable. Be sure to use high quality cables – HDMI should be labeled Ultra or Premium, USB-C cables should be rated for high-speed data transfer, etc. Also, cables should be as short as possible (≤1 m for most cables, <0.5 m for Thunderbolt 5 cables). That random cable you found in a drawer might or might not work. 

Some users have found that the issue was caused by a corrupted preference file. To test that, you can delete the relevant files with the following steps (macOS will automatically recreate a new, clean one):

• Select Finder > Go menu > Go to Folder, paste the following

/Library/Preferences

• Delete the file named "com.apple.windowserver"
• Again select Finder > Go menu > Go to Folder, paste the following

~/Library/Preferences

• Delete whichever of the two files you find:
  • In the Preferences folder that opened – "com.apple.windowserver.<UUID>.plist"
  • In the ByHost subfolder – "com.apple.windowserver.<UUID>.plist"
  • (Note that <UUID> is a string of hexadecimal numbers that is specific to your Mac)
• Restart your Mac

Source: External Monitor Not Detected After macOS… - Apple Community

Personally, my LG 5K:2K display is working well with my two Macs (one on the latest Golden Gate, the other on the latest Tahoe), but not directly comparable as it's a Thunderbolt 3 display connected via a TB3 dock.

<< The same monitor, HDMI cable, and adapter work correctly with a Windows laptop. >>

Simply stated, the Mac has MUCH higher standards than a PC.

If anything is not good enough to avoid transmit errors, the display will be reduced in resolution, then dropped entirely.

Running higher resolution (on a Mac) than 4K at 30 Hz at 8 bits/color requires special HDMI cables and very special adapters.

what exact model LG display?

HDMI above 4K at 60 Hz uses HDMI 2.1, which switches to a signaling method very similar to DisplayPort, but uses higher voltage levels.

ULTRA or 48G labeled cables are REQUIRED.There is no official guidance for cable lengths, but similar limitations to USB or DisplayPort would be Prudent.

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When adapting display data from most USB-C ports using ordinary adapters, each display interface uses a different set of standard speeds, as part of their standards. Each allowed speed must fit inside the maximum speed of USB 3, which is 20 G bits sec.

for HDMI, the highest standard speed that can be supported by the protocol (when starting with USB-3) is 14.4 G Bits/sec. That allows a 10 bits/color 4K HDR display to run at up to 50 Hz. IF your display supports a slightly different reduced color space, it MIGHT be able to run as fast as 60 Hz in a reduced color space under ideal conditions.

Your specific Mac has USB-4 ports, but using that extra speed requires an adapter rated for BOTH higher speeds and Much higher Voltages of HDMI. In general, that can not be accomplished with a dongle-style adapter -- it generally requires a Docking device with its own power supply.

Not with your specific combo … but with a MBP paired with another LG Monitor:

I found it to most reliably “connect” if I first allowed the laptop to fully startup …

… then powering-on the monitor always produced good results.