As far as I know, the only profile provided for Fuji cameras is Adobe Standard. If you want to use the Fujifilm Classic Chrome you would have to shoot JPEG and choose that profile in your camera settings and it would be embedded into the JPEG image.
They aren’t supplied by actual .dcp files but ACR 8.4/LR 5.4 added various Camera Match profiles for Fuji cameras. See the release notes:
It seems that the X-E2 didn’t get the Classic Chrome profile until mid-December, about the time LR 5.7.1 was actually released, so there wouldn’t have been any time for Adobe to add it.
Adobe introduced Camera simulation matching profiles to Lightroom in Feb 2014 see quote from the Lightroom Journal.
"Added Camera Matching color profiles (PROVIA/STANDARD, Velvia/VIVID, ASTIA/SOFT, MONOCHROME, etc.) for the following Fujifilm cameras:
- Fujifilm X-A1
- Fujifilm X-E1
- Fujifilm X-E2
- Fujifilm X-M1
- Fujifilm X-S1
- Fujifilm X-T1
- Fujifilm X-Pro1
- Fujifilm X10
- Fujifilm X20
- Fujifilm XF1
- Fujifilm XQ1
- Fujifilm X100
- Fujifilm X100S
There profiles should be available in the camera calibration options if you are using raw files from the camera. I am not seeing "classic chrome" mentioned but are the others available?
Here is a reference for the Classic Chrome being released in a firmware update on Dec 18th, 2014:
Adobe have Classic Chrome available for various cameras won’t occur merely because the camera can do it, and this triggers something in Adobe software, the Classic Chrome will appear as a camera-match profile when Adobe adds it, and that wouldn’t happen until after Adobe has the particular camera in hand and can reverse-engineer the treatment and then add the effect in the next release of software after it’s ready.
Understood, I guess then the user will have to wait and hope that Adobe provides an update to the X-E2 camera matching profiles.