It seems that when running a 32-bit application on a 64-bit machine queries to HKEY_LOCAL_MACHINE\SOFTWARE\ are redirected to HKEY_LOCAL_MACHINE\SOFTWARE\WOW6432Node\ so the registry keys should be as follows:
[HKEY_LOCAL_MACHINE\SOFTWARE\WOW6432Node\Visual Sciences]
[HKEY_LOCAL_MACHINE\SOFTWARE\WOW6432Node\Visual Sciences\Lemmings Paintball]
"SrcDisk"="D:"
"DestDir"="C:\\Games\\LemBall"
[HKEY_LOCAL_MACHINE\SOFTWARE\WOW6432Node\Visual Sciences\Lemmings Paintball\Beta]
A quick side note, the 16-bit subsystem (NTVDM) does not exist in the 64-bit versions of Windows (7,8,10,11) so 32-bit applications with 16-bit installers cannot be installed without a workaround.
I used a Windows XP virtual machine but there was no need because all of the game files can be copied from the disc (I have the Argentum [Euro] version of Lemmings Paintball, which includes Lemmings 95). Using the above registry keys fixed the state of the autorun/title menu (the `Install Paintball' button is now greyed out and the `Play Paintball' button is clickable) plus it gets rid of the message that Lemmings Paintball is not installed. Unfortunately, clicking the Play button does not actually run the application but double clicking the executable LEMBALL.EXE in the game folder (or on the disc) now works fine.
However, fullscreen mode (shortcut F4) does not work because apparently routines are referenced that no longer exist in Kernel32.dll in Windows 7 onwards. The details of which are discussed on the following two webpages:
https://sourceforge.net/p/dxwnd/discussion/general/thread/1ce69f5937/https://www.vogons.org/viewtopic.php?t=56316