I managed to get this working today!
Backstory:
At the time of my previous post, I was using Solus. Nice little distribution but repositories really quite small so ended up moving to Pop!_OS, which is for the most part extremely similar to Ubuntu but with some tweaks. Now, despite moving from Solus to Pop!_OS, Leadwerks would still not run even when trying the fixes previously mentioned here, so I threw in the towel and gave up.
Present:
I noticed a couple of days ago that there appears to be a new Steam Linux Runtime available - Steam Linux Runtime Soldier. This runtime actually works with Leadwerks allowing you to test your games without the dreaded CURL_OPENSSL_4 error.
From your Steam library, right click on the Leadwerks Game Engine application and choose properties.
Tick "Force the use of a specific Steam Play compatibility tool"
From the list, select Steam Linux Runtime - Soldier
This seemed to work for me.
Notes:
Before trying out Steam Linux Runtime - Soldier, I must mention that I had already previously run the commands as already discussed in this thread:
cd ~/.steam/steam/ubuntu12_32/steam-runtime/pinned_libs_64
mv libcurl.so.4 libcurl.so.4.bak
ln -s /usr/lib/x86_64-linux-gnu/libcurl.so.4 libcurl.so.4