If you want to get technical, lexicographical ordering is a generalized concept, with several variations. Most likely, whatever the ordering you want to call that, it is probably of a lexicographical order type.
I think its a little unfortunate that the design has settled on this ordering since most likely use of these comparisons (at least in my experience and with reference to the CartesianIndex examples) is for bounds checking multidimensional algorithms
Without checking, it looks to me like the behavior is according to the column-major order of Julia arrays. That is, I1 < I2 if in an array A, the element A[I1] comes before the element A[I2] in memory. This is consistent with the behavior you see, although of course there’s not zero-based indexing in Julia. The first example compares the index of an element in column 1 to the index of an element in column 0; the first index comes after the second in memory so it’s not <=. In the second the first index is still in column 1, but the second is in column 2 and so comes later in memory; then the first one is less than the second according to their appearance in memory.