Thank you James for pointing me in this direction, this is solid logical thinking here!

Wouldn't have thought about trying the LS DLL under basICColor soft.
So I ran some tests with various combinations of softwares, DLLs, and VM. Mat was kind enough to send me the CP Discus DLL so I tried it too.
Here are the results :
LightSpace + LightSpace DLL = Nope
LightSpace + basICColor DLL = YES!
LightSpace + CP DLL = YES!
basICColor + LightSpace DLL = YES!
basICColor + basICColor DLL = YES!
basICColor + CP DLL = Nope
I confirmed the results within the two VM setups available to me at the moment :
Win 8.1 under macOS 10.13 using VirtualBox
Win 10 under macOS 10.13 using Parallels
LightSpace DPS v9.0.0.2830 and basICColor display 5.8.1 were both installed at the same time (so no hogging). Probe was connected and rotated to calibration position (·) before software launch.
Two results seem quite strange : the LightSpace DLL is working under the basICColor software although it is not under LightSpace, and the CP DLL isn't working under basICColor software. In this case, the probe just disappear completely from the probes drop-down menu (which list all probes supported by the soft, not just connected ones). The sizes of the DLLs are also interesting, with the LS being 96Ko, BC being 98Ko, and CP being 204Ko.
Note that I only tested the connexion with the probe, and its calibration. I did not performed calibration using the working combinations so there can be hidden bugs with the working DLLs. I'll perform some calibrations under LightSpace to see how it goes.
I don't exclude the possibility of my VM settings preventing the LS DLL to work under LightSpace, but I hope basICColor tests will reproduce the "under LightSpace" part of my setup to assess the capabilities of the DLLs tested.
I hope this can help to identify and solve the issue.