You are right that the lens is a 9mm thread. But the head of a Axiz module, where the diode is pressed in has a 11mm thread. But that's not the point anyway. You need to thread the OD of the back of your heatsink is what I am understanding now. Do you have access to a cnc shop? If not then your best bet is finding someone at CNCZone that will do it for you.
If you have a good drawing of what you need I might be able to work it into my break periods at work and fix you up that way. I am frequently pressed for time due to the work loads on the machines so it may take a couple weeks to get it in. PM me for an email if you want to send me a drawing and try that route.
Clayton