Submitted by Janek Kaseja:

This is the traditional NPS recommended backpacking route, starting and finishing at South Bass trailhead:

https://www.nps.gov/grca/planyourvisit/upload/Royal_Arch_Loop.pdf

This route includes two short out-and-backs to Royal Arch and Elves Chasm, so it is not really a perfect loop or lasso. The route is well cairned, though the descent from the Esplanade through Royal Arch canyon most people would consider off-trail. And of course there is a 20 foot rappel.