This is an excellent run. With moderate grades, steepening only with technicality, the vast majority of this can be run at a good clip. Once above 13,200 ft, the going is rocky and steep, but everything below is Forest-friendly.
Run one mile from Lily Lake Trailhead on Lily Lake Trail over mostly flat, clear terrain before coming to a trail junction with a sign for Lily Lake. Staying left will put you on this trail. In another hundred yards or so, cross a river on some rocks and/or downed trees. Follow the trail away from the river, passing a boulder field on your left at around 10,800 ft.
From here, the grade cranks up. Follow the trail up 600 ft and come to a low-grade drainage to your right. Follow the trail along the gully before running back into the trees. Reach tree line at around 12,000 ft, just about 3 miles in. The going is slower from here.
Drop a hundred feet or so, heading to the left into the basin between Mt. Lindsey
and the Blanca Massif. Follow the mostly class 1, occasionally rocky trail southeast. Come to a flat area around 12,200 ft before continuing back up to reach another flat area at 13,000 ft. It's rockier from here on out. Reach the 13,200 ft saddle between Iron Nipple (13,000 ft, to the left) and Mt. Lindsey
(14,042 ft, to the right).
Follow the trail to the right along the rocky saddle. The northwest ridge is fairly clear, with a brief, steep face about halfway up. The rock here is solid. The gully to the left, which is the standard route, is loose and unpleasant, but makes for an easier descent. Follow the trail, running left of the ridge, onto a talus field below a steep gully. Run up and to the right across the talus, reaching the bottom of the gully in a few hundred feet. Continue up the rocky, loose gully for about 300 ft before coming back to a gravel trail. You may encounter climbers coming from the ridge below. From here, it's just a couple hundred yards to the summit.
There aren't a lot of wildflowers in this area: expect lush forest down low and a grassy basin up high. Marmots and pika are everywhere, though.