It looks from your example images as though it could be a colour management issue. Lightroom uses different colour spaces for the Library and Develop modules, as explained here. (Key excerpt below)

Lightroom primarily uses the Adobe RGB color space to display colors. The Adobe RGB gamut includes most of the colors that digital cameras can capture as well as some printable colors (cyans and blues, in particular) that can’t be defined using the smaller, web-friendly sRGB color space.

Lightroom uses Adobe RGB:

• for previews in the Library, Map, Book, Slideshow, Print, and Web modules
• when printing in Draft mode
• in exported PDF slideshows and uploaded web galleries
• when you send a book to Blurb.com (If you export books as PDF or JPEG from the Book module, however, you can choose sRGB or a different color profile.)
• for photos uploaded to Facebook and other photo-sharing sites using the Publish Services panel

In the Develop module, by default Lightroom displays previews using the ProPhoto RGB color space. ProPhoto RGB contains all of the colors that digital cameras can capture, making it an excellent choice for editing images

Unfortunately, there doesn't appear to be any way to set Lightroom to use the same colour space for both the Library and Develop modules.

To help you adjust your photos correctly for printing, Adobe suggest:

In the Develop module, you can also use the Soft Proofing panel to preview how color looks under various color-managed printing conditions.

and:

When you export or print photos from Lightroom, you can choose a profile or a color space to determine how the colors you see in Lightroom will appear on the device you’re sending the photo to. For example, you can export using sRGB if you’re going to share photos online. If you’re printing (other than Draft mode), you can choose a custom color profile for your device.