BTW, I downloaded the profiles and checked, the profile they provided for Epson Semi-Gloss was indeed a CMYK profile that will not work in Lightroom.
In fact, the 'theprintspace Canson Aqurelle Rag.icc', 'theprintspace German Etching.icc', 'theprintspace Hahnemuhle Pearl.icc', and 'theprintspace Hahnemuhle Photorag.icc', all report as CMYK profiles and are thus not usable in LR.
You can use them in Photoshop, but to tell you the truth, I seriously question their choice of making and providing CMYK profiles vs. RGB profiles for those papers on Epson printers. There may be a good reason, but if they are using Epson printers with the Epson drivers to make the prints, then they made a poor choice when creating the CMYK profiles instead of RGB profiles.
If they are using a 3rd party rip, then that might be a different story, but they should say that (and they don't say much of anything useful on their web site). BTW, all their C-print profiles are correctly RGB.
Are you sure you want to use these folks?