This route description begins from the summit of UN13,140. Mileage and elevation gain are calculated from that spot to UN13,223. Since you will likely return by going back over UN13,140, we have doubled the elevation gain and you'll need to double the mileage.
From the summit of UN13,140, you'll have two clear choices. 1. Follow the connecting ridge north and NE to the UN13,223 summit. The challenging part of this ridge will be the initial descent from UN13,140 to the saddle just below 12,800 ft. "Furthermore" reports on LoJ that the ridge goes at 3rd class. 2. The second choice will be to give up 600 feet in elevation and do a talus descent north off the summit of UN13,140 into a basin, then regain the connecting ridge beyond the saddle and follow it to the summit of UN13,223.
Because one of our party members was reluctant to attempt the full ridge traverse, we elected to do the talus descent. I (Tim) did explore for a short distance along the ridge off the summit of UN13,140 and found that one simple, 3rd class move around a rock tower early on brought me to less complex ridge work. There may have been other, unseen difficulties ahead, however. But since the remainder of our party would not follow, I had to reverse and go back for the talus descent. We also tried to traverse under the connecting ridge near the NW summit on the NE side but found that slope to be precariously loose & difficult.
So, from somewhere about midway between the NW and SE summit of UN13,140, pick a descent path north down the loose talus and scree into the basin below. You'll have a good view of this basin and the entire route over to UN13,223 so you can plot your path early on. Something to steady yourself with like trekking poles or an ice axe comes in handy. Once things begin to flatten out some after about a 600 foot loss, contour north aiming toward the 12,800 foot saddle. Regaining the saddle will not be all that easy. The slope is very steep, vegetation is limited with a lot of gravel and sandy-like soil. Towards the ridge, we had to bypass some rock outcrops. Once back on the ridge, continue north to the false 13,100 foot summit. Though the walking now is mostly on typical, Elk Mountains maroon rock, it was much easier going than the talus descent or scramble back up to the saddle. Bypass the false summit and continue NE to the interesting little summit. The final summit portion has some interesting scrambling on ledges of the layered maroon rock. Some may consider this 3rd class. It's not really exposed so we're going with Class 2+.
The view from this summit of the Maroon Bells across the valley is amazing. The peaks look very formidable and loom over the surrounding landscape. Enjoy the view. It may be possible to continue from UN13,223 to UN13,631. Since we had done that peaks nearly 20 years earlier, we did not spend much time examining the route, but see one of our attached photos for a hint of what to expect. If not going on to UN13,631, then return as you came. If you drop back down into the same basin, the climb back up to UN13,140 will go better if you take an ascending path that will follow some loosely defined ramps through the talus that first swing to the SE, then back south and SW to the ridge crest. This lessens the angle of ascent and may bring you out a little SE of the higher, SE summit. In earlier season, an ice axe may be helpful.
Links to other information, routes & trip reports for this peak that may be helpful.