What are the outer dimensions of the GoPro 3+ lens holder?
I don't have the Hero 3+ but you can measure it with the help of a front picture of the cam and the dimensions of the camera.
Taking the dimensions from here: http://www.dpreview.com/articles/8137555963/hands-on-with-The-gopro-hero-3-black-edition
(5.8 x 3.9 x 2 cm)
And using this picture:


And measure how big the lens casing is compared to the size of the camera in pixels (for example with the Photoshop ruler tool)
We get 35.4 mm for the width for example. So I'd go with a solid 35mm (width).

I measured 537 for the camera and 327,5 for the black lens casing. So the Black Lens casing is 61% the size of the camera. 61% of 58mm is 35.38mm.
You can do the same with the other dimensions.