I am using DXO PhotoLab, version 5 to be exact. This software has been my go-to image processing software since I switched to Micro Four Thirds and upgraded to V5 right away when DXO finally announced X-Trans support with that version. For my very basic style of processing, it is more than enough and I am mostly satisfied with the results.
In addition I'm also using Fujifilm's own X RAW Studio software, however I wouldn't really call it an editing or even processing software, since it basically just provides an interface to communicate with an X-System camera - which also does all the processing. It is quite nice though to experiment with different film recipes, as you can save a virtually unlimited amount of them and since the camera does all the processing internally, you essentially still get sooc jpegs out of it.
I've also used the free Capture One Express version for Fujifilm, which also was mostly enough for my basic needs. I feel Capture One can produce somewhat more pleasing output than DXO, but maybe that's just my imagination.
I have never really tried Lightroom and feel like I am the absolute oddball minority everywhere, so I can't say anything about it. I am not a big fan of their subscription model and that was essentially the major reason why I've never tried it at all.