Well, given the shape of the lake, a single crater doesn't make sense to be the source of the entire lake. But it could be feasible that an explosion could be involved. But we see one pretty major issue with the crater idea... The larger a crater, the more force involved. Since there aren't all that many large craters on Earth not involving meteorite strikes, we'll use some rough numbers from that. a 50m meteorite striking down has created a crater 1200m in diameter. Given that the rounder sections of the lake, estimated from the map, are at least ten times that diameter, the energy involved in the explosion would be enough for major climate change, if not a full-blown extinction event.
Mind you, that could be the event that broke the Old Kingdom. Essentially what we're saying here is that an explosion of that magnitude is massive.
Just estimating using a Crater output calculator we found, a crater about 12 km in diameter, based on dense rock striking porous rock at 72 degrees, would have an energy of 3470 megatons. The biggest detonated nuclear bomb (Tsar Bomba) was about 50 megatons. In other words, the forces involved in a crater anywhere close to 20km in diameter are almost unimaginable.
EDIT: Muddy bottom isn't unlikely. As for climate, look to Sparks.