The minimum FT/GB-ratio is around 1:1. For 1000L you need 1000L of grow beds.
This is not necessarily so. I have a 4,400 fish pond I built and my one and only grow bed is approx. 500 gals give or take. My Koi do just fine and so do my veggies. You can see my system here:- NOW YOU'VE GOT DUCKWEED !

The main thing you have to have is a bio-filter that will handle the fish tank volume regardless of how big the grow beds are. Fish can stand a high count of nitrates but not nitrites. I also grow duck weed in my grow bed and fish pond which helps eliminate some of the nitrates.

As for pulling water from the lake, just for grins, why not get a test kit and test to see what the make up of the lake water is. PH, nitrites, nitrates etc. That will answer that question for you, however I do not recommend piping it to a fish tank attached to your system due to unwanted parasites such as dragonfly larvae and leeches. Also be aware of any pesticide spraying of field crops and also for mosquitoes in your area because those chemicals will be in your lake water.