Is it permissible to listen to religious lectures while working from home, and is it necessary to seek permission from the employer who has granted the flexibility to perform work at any time, given that the quality of work is not affected thereby, and the purpose of listening is to be eager for work and to learn about religion?

If your work as a writer is not affected by listening to lectures, then there is no harm in that for you, and you are not required to seek permission from your employer. The contract between you is for a specific task (writing) and not for a duration of time. Thus, you are in the position of a "common employee" (al-ajir al-mushtarak), whose full benefit is not owed to the employer, unlike a "private employee" (al-ajir al-khass) whose benefit is entirely due to the employer for the entire duration.