Capture One uses the "manufacturer's profile" provided by Fuji for this lens on my version of C1. My version of Lr also uses this same profile ("built in profile applied" in Lr, which is the same thing). I'm personally not seeing any major optical differences in the samples I'm looking at between the two programs. What are some differences you're seeing? If you're seeing a lot of differences in your own images, you may want to raise a bug report to C1 and provide links to the raw images so they can take a look. Often, if the manufacturer provides their own profile, as is the case with a lot of lenses over the past few years, they won't always take on getting the lens on the bench in their labs and building a bespoke profile. If you are seeing major differences as far as optical corrections that need to be brought to their attention in your own work (and you're using the manufacturer's profile in the drop down), it may be that a bug report is an optimal approach to resolving your issue. Here's their link (and you'll have the opportunity to provide sample images). https://support.captureone.com/hc/en-us/requests/new
Just a suggestion and in no way am I saying that you shouldn't request the lens support, certainly if the manufacturer's profile isn't up-to-scratch (and sometimes, that's the case).
EDIT: Definitely make sure the profile isn't "generic" or "generic pincushion distortion" as these aren't good "out-of-the-box".
Capture One uses the "manufacturer's profile" provided by Fuji for this lens on my version of C1. My version of Lr also uses this same profile ("built in profile applied" in Lr, which is the same thing). I'm personally not seeing any major optical differences in the samples I'm looking at between the two programs. What are some differences you're seeing? If you're seeing a lot of differences in your own images, you may want to raise a bug report to C1 and provide links to the raw images so they can take a look. Often, if the manufacturer provides their own profile, as is the case with a lot of lenses over the past few years, they won't always take on getting the lens on the bench in their labs and building a bespoke profile. If you are seeing major differences as far as optical corrections that need to be brought to their attention in your own work (and you're using the manufacturer's profile in the drop down), it may be that a bug report is an optimal approach to resolving your issue. Here's their link (and you'll have the opportunity to provide sample images). https://support.captureone.com/hc/en-us/requests/new
Just a suggestion and in no way am I saying that you shouldn't request the lens support, certainly if the manufacturer's profile isn't up-to-scratch (and sometimes, that's the case).
EDIT: Definitely make sure the profile isn't "generic" or "generic pincushion distortion" as these aren't good "out-of-the-box".