Since I do get a lot of questions as regards this above question, I will like to mention that University of Lagos Postgraduate programme do not require you to provide some documents immediately you seek admission for the programme.
Though you most be in possession of all required documents, the most important documents that you need include your statement of result or notification of results to apply.
If the statement of result or notification of results is available you can use that to apply for the Postgraduate program but you will need to provide your transcripts or original certificate alongside with your NYSC certificate or exemption letter when you are admitted for successful registration as a Fresh Student.
With this being said, it is also important to note that Unilag Postgraduate Program is very competitive due to the number of applicants to the prestigious school . For you to have an advantage you will need to get prepared properly with the needed materials.
The most important material that is time tested is the Unilag Postgraduate Past Questions and Answers in any of your desired Postgraduate program due to some departments repeating their questions . You can check yours HERE