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Numerous critics of Finney have quoted exactly this same text out of context. Read Finney before criticizing Finney. Don't read the critics and place quotes taken out of context out for review. Finney distinguishes in this lecture between permanent justification and present justification. His point is that dwelling in sin is not indicative of the salvation experience, and we can't think God saves us so we can continue to live in sin. Bible-believing Calvanists and Arminians agree that justification is not a license to sin, which is the point of Finney in this comment. If you disagree with that, you disagree with Paul, as was well-documented by Finney in quotation after quotation from the writings of Paul in that Lecture. While Finney was an Arminian in theology, he was far from being the heretic you make him out to be.
Read the book. You might find your faith enriched.
Finney also stated:
"10. This state is to be attained by faith alone. Let it be for ever remembered, that 'without faith it is impossible to please God' (Heb. 11:6), and 'whatsoever is not of faith, is sin' (Romans 14:23). Both justification and sanctification are by faith alone."
So, did he promote a salvation by works? Hardly. One can only understand what he was teaching when the entire context is read, not when a sentence is yanked out and tortured. How can one understand the Bible if it is studied that way also?
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2 Tim. 3:16--All scripture is given by inspiration of God, and is profitable
for doctrine, for reproof, for correction, for instruction in righteousness.