For anyone who is interested, these are the Lightroom settings that enabled the print size to match the actual image dimensions:

1. Resize the image in Photoshop CS5 using Perfect Resize. 
2. In the Lightroom print module, I chose these settings:

• Cell size set to match the image dimensions.  The photo was sized to the same aspect ratio as the cell size/print size.
• All the margins are set to 0.13, which is the minimum.
• "Zoom to Fill" is checked.
• Page Setup:  choose paper size and manual - rear.  Make sure you do not choose borderless unless you are printing a borderless photo. When you print borderless the printer driver enlarges the photo slightly to ensure edge to edge coverage.

Jogi73 - that's a good question about resizing in Photoshop first.  I should have written a more generalized list for enabling the print size to match the actual image dimensions.  I've incorporated your steps above - where can I switch off the contour (German "kontur") as you suggested?

Here is another draft:

1. Is the image in the right proportion to print?  Does the aspect ratio of the image width and height match the desired cell size in the Lightroom Layout Panel?  If you are printing for standard mat and frame sizes, this may be a concern. Cameras capture images in a variety of aspect ratios that don’t necessarily match common print sizes.  For example, in a full frame camera the number of pixels may vary from model to model, but the ratio of the long side to the short side will always be 1.5:1 or 3:2.  Digital compacts often have a ratio of 1.33 or 4:3. 
   
   • If the answer is no:
     
     • Blank spaces fill the areas where the aspect ratio of the photos and the image cells don’t match.  You can also set an option so that photos completely fill the space within an image.  When this option is selected, portions of the photos (especially vertical images) might be cropped to fill the aspect ratio of the image cells. (source: Lightroom 4 documentation accessed with Print Module)
     • In the Develop Module, you can crop the image to a specified aspect ratio.  This will enable you to manually choose what is cropped.
       
   • If the answer is yes:  proceed to Step 2
     
2. Do we have enough pixels to get an acceptable print quality in a particular size?  For example, if I am taking a photo from an iphone and making a print size of 17 in x 22 in, then I go to Photoshop, and use the plug-in On-One Software’s Perfect Resize (formerly Genuine Fractals) to crop to a specified aspect ratio and resize.   Photoshop can do upsampling as well.  I am not sure if Lightroom can do this upsampling.
3. Now for printing in the Lightroom Print Module.  To print the exact dimensions of an image, here are the key selections:
   
   • Image Settings:
     
     • Check  “Zoom to Fill”
     • Check “Rotate to Fit”
       
   • Layout:
     
     • Margins set to minimum size
     • Cell size is the desired print size according to the aspect ratio of the image.
       
   • Page Setup:
     
     • Make sure that “borderless printing” is disabled in the printer.  When you print borderless the printer driver enlarges the photo slightly to ensure edge to edge coverage.
     • For the Epson 3880, choose the paper size and manual – rear.