Is this a simple case of the "TO" banner missing above the CA-190? For as long as I can remember, CA-136 has always been co-signed with CA-190. I know that historically, what is today CA-136 was once CA-190, but that hasn't been a factor since the 1950s. The most prominent signage is seen directly from US-395.
Wikipedia says that the old LRN 127 included a branch that deviated from the trunk: around the northeast side of Owens Lake. That would obviously be CA-136, so perhaps the signage reflects this, though it seems to be an error regardless.
It should have a "to" but for some reason doesn't. Either way, given all the "Death Valley" control signage that is present I suspect it is intended to aid travelers to the Park from Lone Pine. CA 136 lines up pretty well with the relinquished portion of CA 190 along Horseshoe Meadows Road west of US 395.
https://flic.kr/p/VWbx19