a question :
for example I am building a simple matrix profile for ACR/LR -single illuminant, CM+FM+curve, nothing else... I have a target, measured (spectral data) + a light (H3200K) & filter (80A), measured (spectral data) = .sp
now my exercise ends with (a simple case) :
dcamprof make-profile -i <.sp file> <.ti3 file> <profile.json>
dcamprof make-dcp -t linear -L -c "SONY ILCE-7" <profile.json> <profile.dcp>
does -i <.sp file> in this case bring any benefit for ForwardMatrix really in addition to having a "better" ColorMatrix which provides more logically sane temperature/tint values in ACR/LR UI (slider values) - but ColorMatrix does not do anything with color transform so to say (only ForwardMatrix does, after WB of course), it certainly helps somewhat to a user with a "proper/right/you name it" starting point for WB corrections in UI ? <.ti3 file> has raw RGB data from a target shot and spectral data from target measurments... it seems to me that ForwardMatrix is the same no matter what illuminant I use, right ?... but shall it be so ?
Calibration illuminant has no effect on the ForwardMatrix. It will only affect the ColorMatrix and thus it's ability to predict the correlated color temperature, which is a task specific to the DNG color pipeline (ICC will only use the forward matrix and the calibration illuminant is 100% informational, it has no effect whatsoever).
If you have a single illuminant profile the DNG pipeline does not need to know which temperature the CM was designed for, as it has only one to choose from. When making dual illuminant you need to specify EXIF lightsource so the CM is tagged with a designed temperature. You can't choose any temperature, as the temp is just a table lookup on the EXIF lightsource. Run DCamProf without args to see a list of them.
Currently it's a bit messy, your workflow would be to make the profile with the spectrum (which causes the XYZ reference values to be regenerated from spectra), but the resulting DCP will then have "Other" as calibration illuminant which will work for a single illuminant profile but not for dual, so then you need to use dcp2json/json2dcp to replace that with whatever EXIF illuminant with the closest temperature. It doesn't matter if the light is called "fluorescent" or whatever, DNG only translates it to a CCT value, no spectral shape is taken into consideration.
If the measurement data is the same, the forward matrix should not change if you specify a different calibration illuminant, yes that is correct. The reason for this is that the forward matrix specifies conversion from white-balanced camera RGB to XYZ D50, that is always D50 regardless of calibration illuminant, that is the same way as ICC profiles do. The reason one always goes to D50 is that it's more well-defined to convert further, eg to RGB for your screen and printer.
That is, colormatrix is only about the profile's ability to estimate the CCT the chosen white balance corresponds to. How much of a value that is in the Lightroom user interface I guess is a personal thing. I don't use Lightroom much, but I guess you typically start off with "As shot" white balance, and the profile won't affect the WB multipliers provided by the camera, if the color matrix is off an incorrect temperature translation will show though. If you would apply a processing preset (or whatever it's called in lightroom) which has a temperature and a tint in it the profile will affect the result as Lightroom will calculated the multipliers by using the colormatrix.
When you make a dual-illuminant profile the derived CCT will be used to mix your two forward matrices, so if you have StdA 2850K and D65 6500K, and the color matrices says the white balance is 4675K (exactly inbetween) the average of both forward matrices will be used. So in that case the color matrix has some effect on the actual color conversion, but only then.
Well there's also those ancient DCP profiles which did not have any forward matrix, in that case the color matrix has a direct effect on color rendition of course, you can make such profiles with DCamProf but I don't recommend it. Forward matrices was introduced by Adobe, maybe because they realized that the ICC way was actually better... binding to D50 gives more robust color conversions.
EDIT: corrected some statements on illuminant temperatures to not confuse future readers.