It's important to remember that project closure is a key output of administrative closure.
Here's a list of the criteria necessary to ensure project closure:
Benefits of Lessons Learned and Why They Are Valued by PMI
You should know that lessons learned are an output of administrative closure. The PMBOK defines lessons learned as any learning gained from the process of performing the project. Lessons learned are considered to be a project record.
It is important that you include both positive and negative information about the project. This will allow future projects to duplicate the constructive aspects of the project and to avoid similar downfalls or mistakes.
Documenting the lessons learned should not be delayed until the end of the project. This type of information should be logged throughout the project lifecycle in the project's PMIS, so that useful information is not lost and future projects can benefit from the historical data.
When Administrative Closure Should be Performed
It is important to perform administrative closure at the end of each phase in a project. As was mentioned regarding lessons learned, if administrative closure is delayed until project completion, valuable information will be lost.