This apparently has either been fixed or is a lot better now. We are currently using Paper-Spigot which is a far better optimized version of a Minecraft server backend, and I have been looking fairly regularly on updates on the lag situation. So far I have not seen any big console warnings or have heard any complaints, which is great news!
Hopefully it stays this way, but will still be keeping a super close eye on it.
I have spent the last few days trying to diagnose and study lag problems with the Minecraft server, after stripping a series of plugins after plugin, I have ultimately determined the root cause to be what others are saying, that it is simply a result of the 1.14.X update!
The gist is that Mob AI and entity calculations are a bit screwy and are causing issues with lag, and the reports are consistent with the server reports as well. To try and combat this, I have adjusted some settings to try and help reduce on problems, but I cannot guarentee success. One important thing of note, when you die, your items are now put into a chest. This is to help A. compensate for lag deaths, B. reduce entities existing on the world.
This change may not be permanent, but it will be here for now until further notice!