That, if true, would predate the formation of the lakes as a source of water.
Still a great many questions remain. How fast water can erode the stone, how long water has flowed through this particular gorge and a constnat source of water.
I wouldn’t preclude anything just yet.
You don't need a lake as a source of water - 10 inches of rain a year is enough. If you want to see some interesting topo maps, google 'Steens Mountain' under google maps, change to terrain, and then check out some of the valleys on that fault block mountain.
They've already side-stepped the fact that basalt is some of the densest material on Earth. It would definitely be eroding much slower than the surrounding material.