The current dictionary entries for 'orthogonal' all have mathematica senses (geometrically perpendicular, linearly independent).
Though not an official semantic entry, the word is used metaphorically to mean independent in the non-mathematical sense of not-related or not dependent. This is often to distinguish from situations where X depends on Y. If X and Y are related, but X doesn't depend on Y and Y doesn't depend on X, then they might said to be orthogonal.
You ask with respect to word pairs. In lexical semantics, there are a number of terms to describe relations between two words. 'Synonym' is for words which have a lot of semantic overlap and might replace one for the other. 'Antonym' is for two words which are on the same scale or dimension but at opposite ends. 'Hyponym' is for a word which describes a subset of concepts described by another word. And there are others.
Back to 'orthogonal'. let's take the positional words left, right, in front, behind. Left and right are opposites, and front/behind are also. You're asking about, say, what the relation is between left and behind. "Is 'left is orthogonal to behind' correct usage?".
Maybe that's a straw man, but the more appropriate usage would be to compare the dimensions, not the words themselves. This example is a little too literal (because they are really directions which are what the linear algebra use of orthogonal is trying to compare).
'Orthogonal' could be used coherently for comparing say gender vs ancestry. 'brother' and 'sister' are both gendered versions of 'sibling' (and so hyponyms of sibling). 'mother' and 'grandmother' are gendered versions of 'parent' and 'grandparent'. So I would say it is poor usage of the word 'orthogonal' to say 'sister is orthogonal to parent' but better usage to say that ancestry is orthogonal to gender.