Is it permissible to masturbate once a week with the intention of sleeping and for therapeutic purposes, in the event of being unable to sleep due to excessive thoughts of lust, and not experiencing a wet dream, knowing that practicing it previously helped with sleep?

Your problem lies in dwelling on lustful thoughts and not being prepared to confront them. You are not permitted to treat yourself with masturbation. Instead, you can take medication to reduce lust. Masturbation has severe harms, such as insomnia and depression. We advise you to make the supplication: "O Allah, I seek refuge in You from the evil of my hearing, and from the evil of my sight, and from the evil of my self, and from the evil of my semen."