Everytime someone tries to interact with DGETRF for the first time, they look up the API (at http://www.math.utah.edu/software/lapack/lapack-d/dgetrf.htm... maybe) and read, "The leading dimension of the array A. LDA >= max(1,M)." Which tells them nothing, so they keep digging through the documentation. Maybe they check the user's guide, https://www.netlib.org/lapack/lug/node116.html and they read "However an assumed-size array declaration has been used in the software, in order to overcome some limitations in the Fortran 77 standard." but sadly their journey is still not over because none of these source have characterized it as you are (as an array stride due to memory layout). Nor named it appropriately. They still have to keep digging to understand it as a stride.
Its name reflects the fact that it was common to oversize the allocation of the memory for the matrix and then LDA > M of course, because in fact LDA = M_MAX. The leading dimension of the matrix in memory (the stride if you were dealing with a 1-d array). If they are lucky (as I was), they will have access to some of the older software that was doing this and they can see what the purpose of the argument and the rationale of the name is. That this also enables one to focus on a sub-block of A and give a stride value. But certainly that isn't the "leading dimension of A". It is the leading dimension of A precisely when A is a bigger matrix and you are focused only on the upper block because of static allocation of A.