Is Ra'atib, who withdrew his registration for an apartment but whose name remained registered, entitled to claim a right to it after his name won the lottery thanks to Ahmad's payment of the required amount without Ra'atib's knowledge, and does Ahmad have a right to this apartment?

The sale was not concluded in the first place. The amount paid was a guarantee of serious intent to purchase. Ahmed's payment of the amount without Ratib's permission is an infringement upon Ratib's right. The matter is in Ratib's hands. If he waives his right in favor of Ahmed, then praise be to Allah. If he does not waive it, no one can compel him, for the Prophet, peace and blessings be upon him, said: "The property of a Muslim person is not lawful unless given with his willing consent."