It should use the sim’s data by default. If you have Navigraph, you have the option of injecting its data into LNM so that your sim and LNM are in synch.
If you use Navigraph then it updates Little NavMap, otherwise I think Little NavMap uses an older AIRAC cycle.
I think I may have seen the same thing last night, but not really understood what I was looking at.
In LNM, I added a route between a VOR, and an airport. The magenta line showed this course as 241. Using the VOR to navigate this, depending on whether I was tracking 240 or 241 I would be above or below the magenta line, but never on it.
I’m not certain that’s related to what you are discussing though, but it didn’t seem right to me.
If anyone knows how to dig into the MSFS data and pick out the value for the declinations, they can be compared to the FAA site
https://enasr.faa.gov/eNASR/nasr/Next/NavAid
Just pop the ID in and under navigation use you’ll see the magnetic variation as published. If this differs from the base MSFS default data then this is the issue.
If this problem occurs with navigraph too then I’d do the same.
Edit: an easier way to check this would be to compare the course LNM gives you to the official FAA charts on Skyvector.
Test down in South New Zealand. The Magvar there is like 25 degrees… should be VERY obvious then if its True North / Magnetic North issue.
Note: If it were an A2A Plane, with steam Gauges, it would be a Feature if the VORs seemed a little inaccurate (out by a few degrees)…, as the Instruments in Real Life are not 100% Precise.
Should be quite easy to HACK (Modify) one of the gauges, to read the current locations Magvar. (in a non DRM protected plane)
I did this in FSX, when i was doing some development work
Or in MSFS, add a line in any Gauge’s js to display the Magavr in the Developers Mode Console Log - maybe every time the gauge does something unique and not to often. Whatever.
…
I do not use navigraph and still have this issue. So it is NOT navigraph related.
Just completed a flight from KDEN to KMLI. Flew the approach to RWY 27 via the MZV transition, which uses radials from two VORs (MZV and CVA) to fix the IAF for RWY 27. It seemed to work perfectly for me, though the “new” slow turning AP forced me to override and hand fly the approach once I got deep into the ILS feather. Other than that, the APR function on the G3000 seemed to work better than it has been working: glideslope indication and capture seems to be fixed.
But to get back on point, the VOR radials don’t seem to be drastically off, if at all.
Approach plate attached if you’d like to try this at home… 
Could be me.
Having Manual VOR Navigation issues in the FBW A320NX.
After take-off it seems to work for bit.
After moving between a few VOR it stops working. Then the sim crashes 
Trying different ALTS etc etc.
I’ll know more after a bit.
A lot of the ILS approaches now seem to be a couple of degrees out for me. I asked UK2000 to fix one of their airports as a result (which they did), but they say some users are experiencing the problem and others are not. It looks like magnetic variation may have changed, though I’m somewhat confused as to why some users have the problem and others do not.