Mike is right on with the ecosystem concerns, koi burrough into the mud and eat certain plant life in the wild that can cause serious repurcussions. They have even been blamed for rerouting rivers and eroding their borders.
The rocks are basically not desirable for the same reasons as those above posted. The other added concern is that during spawning, male koi press the female koi up against anything they can to push the eggs out of her abdomen so they can enseminate them. The female at this point has released a hormone into the water (similar to scent) that drives the males nuts. The resulting 'sex' is very violent and can injure or kill a female koi if rocks are present.
The other major concern is not merely aesthetic damage from sharp edges, but from a bacterial perspective things can accumulate and grow under rock then take long periods of time to break down, and will emit large amounts of nitrate and nitrite for long periods of time. Nitrate for koi is like poison for you. Not desirable. It can kill them. Under and around rocks also becomes a poop trap and a breeding ground for harmful bacteria that can cause all types of sicknesses, sores, and health problems.
You will probably want to invest in a large UV light to deal with any incoming sicknesses from the lake, but to be honest, I would isolate the system and build a filter for the ponds. Use the lake for source water and a slow trickle of fresh water. Unless you have control of the biological and sickness situations in the lake.
If you are determined to use the lake, invest in a large commercial filter that filters out cysts, reduces hardness, and is low micron with a washable cartridge. Otherwise you may have potentially disastrous health problems for the koi, and water clarity problems.
Hope that helps you. Let us know as things go along, and there are alot of threads here on filtration topics and hardness and ph that will teach you lots. Including how crazy some of us are....
You ph is good for koi, the reds will do well. The hardness issues can be dealt with with a filter. Overall i think your idea is great and will look awesome when done. i would suspect you will quickly become a koi fanatic when you start to see some really nice ones swimming around in your water. They are great pets, and stress relievers that some doctors even say help reduce risk for high blood pressure and heart disease.
The only place I would put rocks in the stream are places where you want a cascading action or waterfall to oxygenate the water. Oxygenation is always good for koi health and water. Lining the edges is nice also.