Basically, you can’t because LR is a database driven system (like Aperture) and doesn’t  provide “round-tripping” of images that have been edited in LR. And even if it did you would lose the detailed editing steps along the way…the two applications are not compatible.

Lots of people have tried various things. Do a search on this site for “acr” to see what they have discovered.

Maybe I’m missing something here, but yes, I certainly can use Lightroom 5 as an external editor. Of course when you use Lightroom as an external editor, it will be working on a tiff file. The process involved export from LR to another folder, then importing back to Aperture. I rarely used LR as an external editor, but often use it as my primary RAW editor. For this process you have to purchase a plug in called Catapult. It will send a copy of the actual RAW file to whatever application you choose. Thus, I can work on RAW files with LR. After processing one can sent on to PS or export back to a Catapult folder for import into Aperture. However, Jim is correct that you loose any ability to go back and see the original LR edits. Of course, there is also a work around to that as well. If you sent your LR edited image to PS as a smart object, then you will be able to see your LR edits anytime, but only in LR or PS.
Not sure any of this is helpful, but there are options if one is willing to go through several steps.
Ken