This route starts from the Golden Trout Lake trail head located at the hiker's parking area in Onion Valley. At the time of this writing, it looked like they may have been closing the original start of this trail and making you first start on the Kearsarge Pass trail. The junction for Golden Trout Lakes trail was a little ways up ( probably less than a mile) and marked by a sign.
Lilley Pass is a scree slog, but this seems to be the most adventurous way to climb this peak. You'll want to head up the Golden Trout Lake Trail. After a mile to two the trail will cross the stream and you'll come to a wet meadow. Cross the meadow and head up Lilley Pass, which should be clearly visible by now. Once at the top of the pass, the summit is in view to your right ( east ). Follow the ridge or the gentle talus slopes to the summit and soak in the views!
Depending on the time of year, you may want an ice axe for Lilley Pass and crampons for extra comfort if so desired.
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