There are several assumptions in your question that are not necessarily shared by everyone.
To start with, not everyone recognizes lexicology as a linguistic discipline. While lexicology is quite common in France, Germany, and Eastern European countries (Russia etc.), it doesn't exist in the USA and it is somewhat new in the UK. See a brilliant article by Uriel Weinreich on this, written about sixty years ago.
Secondly, you're using the terms "total synonymy" and "partial synonymy" in your question. The problem is that different linguists understand these terms differently - assuming that they have such concepts in their theories of (English) vocabulary.
As is, your question has no answer.
However, I can tell you what some experts in lexical semantics (aka lexicology) think. For example, John Lyons talks about full synonymy (identical meanings), total synonymy (synonymous in all contexts), and complete synonymy (identical on all levels of meaning). In his theory, he also has "absolute synonyms" (full, total, and complete synonyms), "partial synonyms" (one of the three mentioned above) and "near synonyms" (not identical in meaning).
Alan Cruse uses different terms: absolute synonyms, propositional synonyms, and plesionyms. etc.