There is no water between Chicken Springs Lake and Lower Rock Creek. It is a sandy, dusty trail, exposed to the sun all day from Chicken Springs until you reach the junction of the trail from Siberian Pass and Soldier Lake trail (junction). From there the trail is okay and level to downhill until Lower Rock Creek
You could, once you reach the junction of the Siberian Pass trail and the trail to Soldier Lake, take the Soldier Lake trail. About 1.3 miles, you cross a small spring feed creek. From there it is .5 miles to Soldier Lake. This side trip is most likely out of your way, however.From there, you just head on down Rock Creek.
I would not count on water from Lower Rock Creek to Lower Crabtree Meadow, which is 5.5 miles.
The climb out of Lower Rock Creek is hard, dug up by horses and mules....dusty.
If you see hikers coming your way, ask about water conditions.
if you need any further info, just post.