CMYK is not a feature of Lightroom. You'd need Photoshop for this.
Thank you. I feared as much.
You can use the Soft proofing feature to get a preview of what the image will look like in CMYK.
First of all, if not already done, calibrate your monitor - you're likely to get unexpected results with an uncalibrated monitor.
Then install the CMYK profile that your printer uses - it may be a profile that you already have installed, or one that your printer will have to provide for you.
In Develop, check Soft proofing on the toolbar (or press S).
Under Profile, below the histogram, click Other, and select the profile.
If you click Create Proof Copy, a virtual copy is created,that you can compare with the original.
The color gamut of CMYK is smaller than RGB, and colors will be less saturated.
Especially blues can turn out very different.
Lightroom 6 and CC 2015 now support CMYK soft proof, which will allow you to review adjust images using the printer supplied CMYK profile. Unfortunately, you can't Export image files using a CMYK color profile inside LR. Your biggest issue is that MS Publisher is not a fully color managed application like Adobe InDesign, Photoshop, Lightroom, etc. Earlier version of MS Publisher support "export" to CMYK PDF, but not MS Publisher 2013. What version are you using? All versions use an RGB working color space so using CMYK image files would cause them to be double-converted (not good!).
Thanks. That's very helpful. I'm using Publisher 2007 so it does have the option to publish to pdf using "commercial" settings but I'm disappointed with the resulting images - especially sky blues. I also think there is a reduction in clarity and a general "yellowing" of many of the images Maybe I'll just have to live with it!
I hadn't discovered the Soft proof feature so thank you. Helpful but it confirms it's very difficult to reproduce some colours in CMYK, especially sky blue! How do professional photographers deal with this in books of photographs??
The inks used on printing presses simply cannot reproduce the full RGB gamut.
As for the problematic blues, I think this has to do with impurities in the cyan ink. You can tweak the colors in Soft proofing view, but getting what you want may be difficult because of ink limitations.
If your images have a yellow cast when printed, I'd question the quality of your monitor profile, try to recalibrate.
If you're seeing a large difference and a yellow tint than you may have a display calibration issue. As Per Berntsen mentioned it's important to use use a good monitor calibrator to insure your display is accurate and LR is using a "compatible" monitor profile (ICC Version 2, Matrix type). Here's an example of a CMYK printed Blurb book showing a ColorChecker next to an actual page in the book. No soft proof correction was performed on the placed image of the ColorChecker in the book. As you can see the two Blue patches are a little lighter and slightly different hue.
You can "adjust" of the HSL sliders to try and correct colors using a Soft Proof Copy, but it can be an exercise in futility (IMHO). Some colors simply can't be reproduced using ANY CMYK printer.