A donationware plug-in called LR/Transporter can do this according to its change log:

Version 4.24, 20th September 2011

Added new tokens to retrieve the full path name of the original image files (only available on Lightroom 3 or higher). Many of you have been asking for this for years, but we've only just noticed that Lightroom 3 finally gives us access to it!

When no money is donated it can only process 5 photos at a time. When a donation is given to the developer this limit is removed.

If you decide to use this software these are the steps needed to obtain a list of full paths from a selection in Lightroom:

1. Download and install the LR/Transporter plug-in.
2. Open Lightroom and select the photos you want included in the list.
3. Go to File -> Plug-in Extras -> Export Metadata using LR/Transporter....
4. Make sure the For each image, create a companion file with suffix is unchecked.
5. Go to the Summary file tab and check Create a summary of all images.
6. Pick a filename for the list.
7. In the middle text box enter the following text: {originalPath}{tab}.
8. You can add a header and a footer in the upper and lower text boxes respectively.
9. Pick a destination for your list and click OK.

This would be the basic steps to achieve what you want. There are probably more advanced functions in this plug-in but I didn't explore them.

I am not affiliated with this application.