The correct term for those kind of service bureaus is "photo lab". A print shop does offset lithography.
Currently in Lightroom you can't convert to color spaces other than Adobe RGB, ProPhoto and sRGB.
You'll need to do that in Photoshop.
First, download the lab's profiles and put them into the correct folder on your operating system. (You need to do this with PS not running; it loads the profiles on launch.)
On Mac, it's /Library/ColorSync/Profiles/
On Windows, right click on the profile and from the popup choose "Install Profile".
In Photoshop, under the Edit menu, select "Covert to Profile". In this dialog box, choose the lab's profile. Use Adobe's ACE Engine, Perceptual Intent, and Black Point Compensation. If Dithering is available use that too.
Save your converted file in the format requested by the lab. Make sure to use internet-friendly names (no spaces or special characters.)
You're now ready to upload or burn to disc.