Typically the semicolon is used to separate two independent clauses without the use of a conjunction. That much you probably know. In my experience (and this is strictly my opinion, but one couched in years of professional writing), the semicolon serves as a temporal marker — a pause more significant than a comma but not as pronounced as a period. I tend to view it like a fermata in musical notation — it serves a purpose in expressing the rhythm of the sentence as it is to be spoken. It is, to me, an almost purely stylistic marker.
And by the way, you should always read your writing out loud. Doing so can reveal all sorts of poor constructions.
That said, the phrase "in this way" does not invalidate the semicolon in any technical sense. Would I use a semicolon there? No, I wouldn't. But only because to me it feels like there is a full stop between the two clauses. They are related by virtue of being in the same paragraph; they don't need any further help connecting.