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.

Traversing between the Lafayette Campground next to Highway 93 (Franconia Notch State Park) and Crawford Notch, via the summits of Lafayette, Garfield, South Twin, Guyot, and Zealand.  Overlaps in part with the Twins, Zealand, Hale Loop, and the Franconia Ridge Loop.  Shuttle can be done by bus.  The traverse is about 36km and 2600 meters of vertical gain.

A short (2.7km) climb with about 600m of elevation gain that is a popular test piece near Morrison, CO.  The ascent, descent, and "round trip of pain" have Strava segments.  The Duathlon adds biking from/to Golden, start underneath the famous "Welcome to Golden" sign & bike any route to the TH.