As a first approximation, one could probably claim that etymology is the diachronic dimension of lexicology but that would probably be too reductive. This is because to fulfil its role, etymology draws on many other disciplines of linguistics.
For instance, etymology relies heavily on phonology to justify successive forms of words because it needs laws to justify how phonemes morph into one another or even disappear altogether. This in turn even allows the reconstruction of bygone pronunciations and unattested word roots.
It also builds on morphology to explain how people evolve the words they need from the ones they have and semantics because meanings shift no less than phonemes.
It is thus both a fundamental component of and an indispensable contributor to historical linguistics and works in this respect hand in hand with hydronymy and toponymy.
Because historical linguistics adds the time dimension to synchronic linguistics it is one of the litmus tests allowing us to prove or disprove theories aiming at explaining how things are the way they are today as much as at predicting how they might turn out tomorrow.
As such I shall venture that etymology is not only a part of linguistics but even a central one.