From the Lumpy Ridge Trailhead, take the trail that heads northwest (as opposed to the trail that heads northeast towards Gem Lake) for 0.5 miles to the Black Canyon Trail. Turn right (east) onto the Black Canyon Trail and hike for a little over 0.1 miles (passing a large boulder with a bolted rock climb to a roof) until you reach the spur trail that heads north to the base of The Twin Owls. Take the spur trail up the steep slope for 0.2 miles to the base of The Twin Owls. Continue on the trail as it passes The Twin Owls on the east side and wraps around to the north side. Once on the north side, look for a large chasm that you can walk into and then scramble to the back of. This is the Bowels of the Owls route.
Scramble to the back of the chimney, going underneath a chockstone on the way. Once in the recesses of the chimney, begin the scramble/stemming up the chimney. After about 30 vertical feet of climbing you can pop up and out of the chimney on the east (left) side. From there, it's an easy jaunt to the top of the 'East Owl' (the high point of the Twin Owls).
You can return the way that you came, or, for a loop hike, head east once you reach the Black Canyon Trail and take that for 0.3 miles to the Gem Lake Trail. Take the Gem Lake Trail south (right) for 0.5 miles back to the trailhead.