Approach from Lost Lake Slough
From the parking area just north of Lost Lake Slough, identify the summit of East Beckwith Mountain; it is the highpoint directly southwest of where you are. Next, locate the Three Lakes Trail and follow it about a half-mile to Lost Lake. From Lost Lake, continue east around the lake on the Dollar Lake Trail for about 200 yards; then leave the trail and start your ascent south up into the basin.
Route Description to East Beckwith's summit
RT-4 miles and 2809 vertical gain
I recommend continued hiking toward the northern ridge extending towards you from the summit. Once you have ascended up the basin, continue as the grass gradually gives way to large boulders. Continue west up boulders to the base of the north ridge and ascend to its crest at 11,800-ft. From here it is a class 2 hike up semi-stable talus to the 12,432-ft summit. The views on top are spectacular. All of this land looks untouched.
Descend your ascent route.
Five Cirque Traverse
RT 11 miles and 4,300-ft.
If you are interested in the long and scenic route on East Beckwith then continue reading. Do not attempt this route if the weather looks unstable. In fact, only attempt this route if you know of a real strong high-pressure weather system in Colorado. Escape routes from this ridge are not very good. The easiest and fastest way to get off the ridge is to drop to the south, but this leaves you in deep trail less wilderness.
Also, do not attempt to do this route without a good topo map. The traverse back to Lost Lake seemed long on length because of the constant bushwhacking. Having a good map with you and knowing how to read it should be enough to escort you through the dense forest for 3.5 mile back to Lost Lake.
From the summit of East Beckwith Mountain you can preview the rest of your route. The ridge sweeps down and out to another point at about 12,200. That highpoint is your next objective; it is maybe a half-mile away with no vertical gain. From point 12,200 continue west and descend 300 feet to a saddle connecting the ridge to another highpoint. From the saddle, ascend the narrow ridge to Point 12,260-ft. From here there seemed to be a doable escape route down a ridge extending north, it looked very steep and loose. It is better to go on to the next point, which is a mile away.
From the summit of Point 12,260-ft you can preview the remainder of the route. This section of ridge is the toughest part of the cirque traverse. It is close to one mile of even narrower ridge with some class 3 scrambling. Expect another 350-ft of vertical gain as well.
After completing this section, locate the s-shaped north ridge that extends out from your summit. This ridge really gets skinny fast, leaving you with the only option to down climb and bypass some of the pinnacles. Take this ridge until it gets too narrow to traverse/climb and locate some loose, rocky ledges to the right that will aid in down climbing into the basin below. Careful route finding is key here but the difficulty will not exceed class 3.
From the basin, the idea from here is to go east to get back to Lost Lake. The hike back to Lost Lake requires a long and arduous bushwhack with plenty of steep side hilling. But remember to stay as high as you can on the 3.5-mile traverse back to the lake, this will eliminate losing valuable elevation. Staying high also will occasionally give you a view of where you are in relation to where you need to be for there are no trails to follow. Most of this traverse is through trees, but there are a few game trails around that will help with navigation.
Bring 3 liters of fluids for this long traverse. There are no reliable water sources once you past the lakes in your first mile. If you do the loop route and descend the S-ridge you will find a few small lakes that might do the job with a water filter.
I would recommend an ice axe in ealy June to mid July.