From what I've read in a comment, you don't want to hear this particular piece of advice, but I'm going to give it anyway: don't publish it until it's done.
I also publish online and, when I first started, I published the chapters a week after I'd finished them (it allowed me to re-read it with fresh eyes in order to catch mistakes otherwise invisible).
After six months, I was agonising because the path of the story became clearer and I needed to make adjustements to the first chapters that would severely impact the reader's reception/understanding of later events. Characters also became more mature and there were some manneirisms I'd thought cute which I now wanted to get rid of. I also found myself needing to rewrite someone's background from absolute-cliché to something more palatable.
After that, I started writing an entire arch (it can be a novel, or a section of a novel, but it's a whole unit) before publishing it. It came down to writing a chapter one day and publishing it 1-2 months later. It improved my satisfaction with the published work immensely. When I go back and re-read those early pieces, even now I feel happy with them (which does not happen with the work I produced in those very early times). Sure, the stories aren't perfect, and there were some things I might do differently now, but I do not regret them.
Unfortunately, I started writing a saga. After two arcs (an arc more or less equals a novel/novella), I realised I was back at the start (needing to make changes to the first chapters/arcs). Once more, I adjusted my work flow. Nowadays, what I am writing will be published in 6-9 months time, and what I am publishing now was written 6-9 months ago.
I write anywhere from 300 to 8000 words a day (unfortunately I can't write daily) and I publish a chapter every week. My readers have no idea how old those chapters are, but the comments do say they love how I manage to interconnect events, and how smartly I foreshadow things. One comment said (and I paraphrase): "Everything was so well thought out! I had totally forgotten about X [apparently insignificant event at the beginning] and I totally ignored all the clues you left. The ending blew me away but it made perfect sense!"
Even if you plan things carefully, once you start writing, you will always come to a point where you want to make changes. Especially when one is writing thousands of words per day because you get 'in the zone', the story and the characters tend to get a life of their own and they'll often lead your away from the plan (if you had one), because you were probably forcing it to happen. This often means readjustments further back.
EDIT: sorry, forgot to address your questions directly.
What should I do, and how should I do it? Are there good techniques / best practices for reviewing past work? Should I leave sleeping lions lie?
In my humble opinion (based on the experiences I mentioned above), the moment you publish a chapter, it becomes untouchable. In the worst case scenario, you can fix typos.
In the case you decide to rewrite, keep the following in mind:
1. If you rewrite just a paragraph or a dialogue line...
a) add a note to the most recent chapter mentioning that there was a change (if you are lucky, about 1% of your readers will go back and re-read).
b) if the change has an impact (a secret was revealed or an essential clue was given), add a note to the most recent chapter mentioning that there was a change and immediately reveal the nature of the change. Even if the reader doesn't go back, they'll be aware of the situation and won't wonder how the character suddenly knew about the secret.
2. If you rewrite a chapter completely, the effects on the future chapters will be paramount. The readers must be aware of everything that changed or the story may stop making sense. In this scenario, summarising the changes may be too long or impractical. I strongly advise publishing it out of order (with the appropriate apology and explanation) in order to force your readers to check it out, otherwise, only 10-20% of your readers will go back to re-read it (this in the event of you repeatedly telling them to go and check because it's a game changer, if you don't push the envelope, count on 2-5% going back).
Note: Do not use strategy 2 more than once. If more than one chapter needs a makeover, publish it at the same time. If those 2 chapters are not one after the other... it's tricky. Just publish the whole group (so readers can effortlessly re-read the whole thing) at the same time.
Moreover, put yourself in your readers' shoes. You've read a dozen chapters, and then you're told chapters 2 and 4 were heavily revised and changed. Do you remember what went down in detail (especially if the chapters are uploaded once or twice a week)? If you re-read them, will you get bored/annoyed with all the parts that weren't changed? Will the very idea of having to go back be pleasant to you? If the revamped chapters are posted out of order, will that annoy you because you don't fully remember what happened before and you feel the need to check it out but it's too much work?
In conclusion, it will save you a lot of headaches and heartache to simply write on a text editor and publish it at least one month later. It will also save your readers a lot of frustration. Unless the story is excellent, I tend to quickly give up on...
the ones which are published the moment they're finished (it's obvious in the amount of typos and in the flow (it's either wavy, with hiccups or heavily 'not-seamless'), not to mention there are often too many retcons as chapters pile up (one retcon is already too many in my book; readers typically create a mental image and expectation as the story progesses, if the facts start changing midway... )
the ones which are always being adjusted (I'm in the 1% who checks the changes). It gets annoying, especially because readers typically create a mental image and expectation as the story progesses, and if the writer keeps saying they fixed things in the back, the reader must be constantly changing what they thought was the facts. Oh, and it really breaks the flow of the narrative when one's forced to go back and re-read past scenes.
Don't change stuff you've already published.
If you're really unhappy with what you've done and feel the need to make radical changes, apologise to your readers and explain you're revised the whole concept in order to make it water tight. Then delete everything and start anew. Do this only once. If the second version is better, you'll be forgiven.