Is a person who stated that Abu Lahab knew that God is the One, the Unique, the Eternally Besought, but arrogantly disbelieved in Him, considered to have made him a believer, and is he required to renew his Islam due to this statement, even with his affirmation that Abu Lahab is a disbeliever and an idolater?

You made a verbal error when you attributed the saying "there is no god but Allah" to Abu Lahab, but you were correct in meaning that he did not deny the existence of God; rather, he did not একক His oneness. This error is not considered disbelief on your part, and you did not intend to affirm faith for him, and you are still a Muslim. It appears you are afflicted with waswasah (obsessive whispering); so, turn yourself away from it, for Allah does not hold one accountable for it. We advise you to supplicate and ignore it, and to consult a trustworthy psychiatrist.