I have been suffering from the issue where the LG monitor does not wake up on my Macbook Pro for a long time. I've read numerous other comments in this thread and elsewhere from people having a similar problem. Mac updates did not fix anything for me but a while back I bought a SECOND LG 5k monitor because I'm a sucker for pain and figured I would return it if it exhibited the same behavior.
This leaves me in an interesting position because I have two of the exact same monitor and ONE has the problem where it does not come back on when the computer comes out of sleep/when it's been left alone and turns off for a while and one does. Using the screen manager software I determined that the one which works properly is using software version 3.06 of the software whereas the one which has this problem uses version 3.04.
I also determined that when you push "update" in the screen manager software, it tries to reach out to a URL which now doesn't work, and in response to not getting anything back, says that the software on the monitor is up to date. This means that on my monitor which has an older version of the software, I can push update and it says everything is up to date - but on my newer monitor, I can plainly see it has a later version of the software.
What you must do is get a file version of the update, and use that method to update the software. So now my request to everyone here: Does anyone have a downloaded version of the 3.06 software? I found other links to someone who posted the 3.04 version link and it still works, i was able to download it, but it's the same version that's on the monitor already. If anyone has the link specifically for version (3.06,1.13,5237,3.04,0.1e) or higher I believe I can install that on the monitor and confirm that this problem is caused by the monitor software.