First of all, you should apologise to your previous employer. While you didn't have to divulge why you were leaving, you lied to them. Don't attempt to justify why you lied.
It would be far better to take a softer approach. You should write up the experience letter yourself, and email it to him for him to sign. You want to make this as easy as possible for him.
If you need it to complete your education, determine what exact details they need and ensure you include the absolute bare minimum.
If the employment happened in Germany, you need to ask for a Arbeitszeugnis. Knowing the word for it may spur him into action.
Unless you need it right now, there is no need to press them. If it does become quite a pressing issue, you can remind them it's a legal requirement, though I would only go down this path if all else fails.