What is the "Module" of a LEGO gear?
Quick answer: LEGO gear module is 1 (metric).

See Section 3.4 at this link: http://bdml.stanford.edu/Main/CrawlerNotes

The consensus seems to be the following:


Lego gears have a metric module of 1, which is the same as a pitch of 25.4 teeth per inch of diameter.
Pressure angle is likely to be about 20 degrees. (This is the most common angle with modern gearing.)
Face width is approximately 1/8 inch. Perhaps more precisely: b = 0.14 inches? - according to a measurement somebody took with calipers in 2011. But note that not all LEGO gears have the full face width. In particular, the crown gears (LEGO's version of bevel gears) do not have a full face width.


From http://orionrobots.co.uk/Lego+Specifications: 


  In the Lego system, technic gears have a ratio that the number of
  teeth are 8 times the diameter, or 16 times the radius in stud pitch.
  Conveniently - the number of studs, and Diameter in Millimeters seem
  to be the same. Note: one "stud" is 8mm. So: 16 tooth gear is 2 studs
  = 16mm => diametral pitch = 1mm.


Also, I have personally 3D printed custom gears with a pressure angle of 20 degrees and a module of 1, and these meshed perfectly with my other LEGO gears.