Implementing ITIL is an oxymoron. As such, an organization will never implement ITIL.
Implementation implies that it has been installed and can now be used as we move on to something else. ITIL is not a tool; it’s a way of working to deliver services to meet business needs. This way of working involves adopting a culture of service that focuses on the business outcomes instead of technology. This culture evolves as the business needs evolve.
Additionally, ITIL promotes the concept of continual improvement. Continual improvement has no end and will never be complete. There is always something to improve.