You can't "fill a lake to excess." The word "excess" implies "more than" and you cannot fill a lake past its capacity. You can fill a lake to capacity, and the additional water will be excess water.
Depending on what you mean, you might use a different word.
"The heavy rain last night filled the lake to the brim; if it keeps raining, a flood will occur." means the lake was filled to, but not in excess of its capacity.
With respect to your original sentence, if you could somehow "fill a lake to excess," a flood would be implied because there is more water than the lake can hold and therefore there already is a flood.