In 2013, we actually combined Middle Pt. with South Lookout Peak, having done S. Lookout first. So Middle Pt. could be easily sequenced with S. Lookout. However, since many may not be interested in doing this soft-ranked summit, we are treating it here as a separate climb with Clear Lake as the trailhead.
From either of the two parking areas on the east side of Clear Lake, follow the trail that leads off to the north like you were heading for S. Lookout. At about 12,200 feet elevation, veer off the trail heading more NW, then west, contouring over to a large couloir that separates the main summit of Middle Pt. from a false summit to the north. This is a very prominent and easily identifiable couloir that appears to offer some tundra for footing most of the way up. Contour just above a rocky outcrop to reach the couloir then begin the scramble upward.
If coming from a climb of S. Lookout, as you descend back to Clear Lake, lose about 700 feet in elevation before beginning your contour westward over at about 12,700 ft. This avoids most problems and keeps you largely on tundra until reaching the same couloir.
While the couloir looks easy enough from below, it's not as secure in footing as you might wish. Staying in the middle of the gully was tiring and the footing was difficult and very loose, so we eventually migrated over to the south wall that we could use for a handrail at times and where we found a little more secure footing. At the head of this gully, we had no clear idea of how we would continue to the summit. The top of the couloir/gully is the technical low point saddle between Middle Pt. and S. Lookout Pk. One quick look to the west side of the ridge proved that option to be ruled out – shear cliffs. So from the saddle, we hiked up a little to the south and then followed a ledge-like system back to the east that led us around an intervening knoll just north of the summit that on the map measures 13,180 ft. Rounding this next section, we entered another narrower couloir that briefly led us to another saddle/col. From here, an easily discernible route led us to the summit. It was almost all on fairly secure rock as we followed another ledge around to the west a little and then ascended on 2nd and mildly 3rd class rock to the summit.
From this sporting little summit, you'll enjoy a splendid view of Clear Lake below and the surrounding summits. Of most interest will likely be South Lookout, looking back to the north, followed by V.2 and V.5. Descend as you came. It will go quickly. From the lake, most reasonably strong groups could complete this summit in about 2.5 - 3 hours.
Links to other information, routes & trip reports for this peak that may be helpful.