I cannot find it now as the book(s) are huge but it is all about (the Lange love of) symmetry. This certainly started with their pocket watches.
Using 'IIII' creates more visual symmetry with the 'VIII' opposite it on the dial than 'IV' does. Using IIII also means that only I is seen the first four hour markings on the dial, V is only seen in the next four markings, and X is seen only in the last four markings, creating radial symmetry.
Simple and elegant like the Richard Lange!