Yeah, it's pretty easy with Lightroom and as Andrew says, you won't need to enlarge anything. Just right-click on your image and go to the "Export…" menu. I would export a full size 16 bit TIFF, because they have much more colour information - which translates to smoother colour transitions & minimal likelihood of banding - than JPEGs.
In the File Settings section of the Export window these settings should be fine:
Format: TIFF
Compression : none
Colour space: sRGB or AdobeRGB (whichever you normally use, sRGB is more common)
Bit Depth: 16 bits/component
In Image Sizing, make sure the "Resize to fit" checkbox is not ticked. Resolution is not relevant.
Output
Sharpening - up to you. If you're
sharpening for print, you need to specify gloss or matte.
That's it basically. Save it to your Pictures folder, or wherever, then burn it onto a CD or put it onto a USB stick and take it to the printer.