Sola is not the goal of lasu. You don't want to leave "sola", you want to leave "min", and how : alone
Lasu min sola = leave me alone.
Bonvolu lasu (kiu) la solan viron, sola = leave (who) the alone guy, alone.
I'm not sure if you understood with this example, but as «sola» is not the aim of the verb, it must not accord.
How do you know whether it should be sola or sole?
I still don't understand the difference.
For some reason, it's especially confusing with sol-. The quick and dirty is that an adjective describes someone - min in this case - so we use sola. If we'd said sole it would describe the manner of leaving.
To me, the given translation, "Please leave me alone", when we say it in English means something like "Stop bothering me" or even "Keep your hands off me". Is that really what the Esperanto sentence means, or does it rather mean "Please leave me on my own", as in "I don't want the company of another person right now"?
I don't see a difference between the two.
In other words - yes, it means the same thing.
You could also say "lasu min en paco."
The sentence is: "Bonvolu lasi min sola".
Why "lasi"? I think it should be "Bonvolu lasu min sola".
Bonvolu is a surprising word for many learners. It's usually translated as "please" - but it's actually a verb. Notice the -u ending. It basically means "Have the good will to...." -- that's why the next verb is always an infinitive.