Easy way to pump lake water is to put some rocks in the bottom of a 5 gallon bucket, put the pump or the strainer pickup in the bucket, tie the hose and wiring plus a retrieval rope to the handle and set it down in the lake.
If it’s easy to get into the lake, you might want a screen with a sock on it to help filter, but it may require cleaning.
Did this for many years watering cattle on some rented ground with a small 2-stroke pump. I filled a 500 gallon tank up on a small rise, then used that to gravity feed two smaller tanks with float valves.
Calcium Hypochlorite pool chlorinating tablets could be used to keep the water from getting nasty in your storage tank.