The problem is not fixed, but I have managed to patch it to make it less of a problem. By using epoxy putty that claimed to be able to set up under water, and some fiberglass tape to hold the epoxy in place, I have managed to reduce the leak from about 1-2 gallons per minute to about 8 oz per minute.
This is a view of the dam:
This is the area at the bottom of the dam where the overflow pipe and the drain valve are:
This is a close-up of the drain valve:
I didn't manage to get a picture of the valve that shows the crack, but it was about 3/16" wide and maybe 1 1/4" long. The epoxy putty and fiberglass tape is
mostly blocking the leak, but the remaining leak is traveling through gaps in the mesh tape and blocking it further may not be possible.
Someone suggested unscrewing the valve from the pipe, then screwing a new one on with the valve open, and then closing the new valve, but they cautioned that if the threads of the PVC pipe end are damaged the new valve may not screw on or might leak. Someone else suggested opening the valve (if possible) and inserting an inflatable test plug into the pipe and then quickly inflating it. Both of these seem like very wet solutions, where if it doesn't work the entire lake will drain.
Several others suggested having a scuba guy take a look and somehow block the drain in the lake, but I'm not sure how to find a scuba diving plumber.