There is only one Lightroom program, just different licensing platforms. I don't know anything at all about that Fuji camera. Have you looked at the different calibration options available for a RAF file from that camera?
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I see the profiles, including Classic Chrome, in LR 5.7 with a RAF from an X-T1 I downloaded from the internet.
I am on the CC Photographer's Plan, so this doesn't verify if the serial-number version has them, and I don't feel like uninstalling this and installing the serial-number version to check. I can say that these are internal to LR and ACR only, because unlike other extra Camera-xxxx profiles, these do not have corresponding .dcp files on disk, so it could be that they are in the CC version, only. One bit of evidence that they should be in the non-CC version is that they ARE there in the CS6-ACR 8.7 plug-in, which isn't CC:
Here is the entry for the LR Blog back when these profiles were first introduced that doesn't say anything about them being CC-only:
One situation where the profiles wouldn't exist is if you are viewing a non-raw (a JPG instead of a RAF) photo, because these profiles are only available for raw files.
If none of this makes sense, can we see a screenshot of your camera profile list in LR 5.7?