There’s an updated Lightroom 4 version of these instructions in the Knowledgebase.
David just posted this very question in one of my blog comments, so I thought it was about time I posted this for reference…
If you’ve deleted your original files, you don’t have backups, and they’re not in the Recycle Bin (Windows) / Trash (Mac), the next thing to check is whether the photos are still on the memory card. If you haven’t reshot the entire card, it may be possible to rescue some of the original photos using recovery software.
If that’s not possible, before you do anything else, close Lightroom, find the catalog on the hard drive, and duplicate the catalog and previews just in case something else goes wrong. Big warning here – LRViewer is offered freely but without support, and although I’ve never seen anything go wrong, backups are always crucial whatever you’re doing.
It’s possible to retrieve Lightroom’s previews using Marc Rochkind’s free LRViewer software, which can be downloaded from: http://basepath.com/LRViewer/ The resulting JPEGs will only be the size and quality of the previews, but they’re better than nothing.
Having downloaded the software from the link above, install and open it. It’ll ask for your catalog location, and once you’ve navigated to your catalog, it’ll open into the viewer window. You can then select the photos and go to File menu > Export JPEGs… to export the previews to the location of your choice.