There are a lot of origins associated with the lake, with the story of Qarun to be the most popular one. The story of Qarun was mentioned in the Holy Quran, in Al-Qasas:76-83.
Verily, Qarun (Korah) was of Musa’s (Moses) people, but he behaved arrogantly towards them. And We gave him of the treasures, that of which the keys would have been a burden to a body of strong men. Remember when his people said to him: “Do not exult (with riches, being ungrateful to Allah). Verily Allah likes not those who exult (with riches, being ungrateful to Allah). “But seek with that (wealth) which Allah has bestowed on you, the home of the Hereafter, and forget not your portion of lawful enjoyment in this world,’ and do good as Allah has been good to you, and seek not mischief in the land. Verily, Allah likes not the Mufsidun (those who commit great crimes and sins, oppressors, tyrants, mischief-makers, corrupters).” He said: “This has been given to me only because of the knowledge I possess.” Did he not know that Allah had destroyed before him generations, men who were stronger than him in might and greater in the amount (of riches) they had collected? But the Mujrimun (criminals, disbelievers, polytheists, sinners) will not be questioned of their sins (because Allah knows them well, so they will be punished without being called to account). So he went forth before his people in his pomp. Those who were desirous of the life of the world, said: “Ah, would that we had the like of what Qarun (Korah) has been given! Verily he is the owner of a great fortune.” But those who had been given (religious) knowledge said: “Woe to you! The Reward of Allah (in the Hereafter) is better for those who believe and do righteous good deeds, and this none shall attain except those who are AsSabirun (the patient in following the truth). “So We caused the earth to swallow him and his dwelling place. Then he had no group or party to help him against Allah, nor was he one of those who could save themselves. And those who had desired (for a position like) his position the day before, began to say: “Know you not that it is Allah Who enlarges the provision or restricts it to whomsoever He pleases of His slaves. Had it not been that Allah was Gracious to us, He could have caused the earth to swallow us up (also)! Know you not that the disbelievers will never be successful.” That home of the Hereafter (i.e. Paradise), We shall assign to those who rebel not against the truth with pride and oppression in the land nor do mischief by committing crimes. And the good end is for the Muttaqun (the pious and righteous persons)
This lake is definitely worth a visit while you are in Fayoum!