Is it considered a sin to collect beneficial and useful books at home without reading all of them, while sometimes benefiting from them by lending them to others?

There is no harm in collecting beneficial books and storing them in a library for reference and benefit, and presenting them to people of knowledge. There is no harm even if many of them are not reviewed. Lending books to trustworthy individuals who will benefit from them is permissible and an act of devotion to Allah, as it aids in the acquisition of knowledge. This falls under Allah's saying: (And cooperate in righteousness and piety) [Al-Ma'idah: 2], and the Prophet's (peace be upon him) saying: (Allah is in the aid of His servant as long as the servant is in the aid of his brother).