I'm sorry to differ with you, Alex, but of the three alternatives you provide, only the second, which begins "Having won the lottery ..." expresses conditionality. You really cannot use "by" or "with" along with "winning the lottery" there to do the job you're wanting it to do.
BUT--even the second option is awkward and overly formal. Well, mostly awkward. Here are some preferable constructions:
If I were to win the lottery . . . [That's just your original sentence with an "if" at the beginning, but it's grammatical English.]
(Colloquial.) If I won the lottery, I'd spend all the money fast. This construction is the one you would be most likely to hear anywhere but at a formal speech or in a formal essay. In other words, even though the subjunctive is proper to use, ("were to win,") often English speakers use the indicative, a breaking of the rules that renders the expression colloquial. ("If I won.")
There are many examples where the subjunctive is proper, but hardly ever used:
- If I were a millionaire, I'd ...
usually you hear
If I was a millionaire, I'd ...
If you should fall in love with him, you would become miserable.
usually you hear
- If you fell in love with him . . .
Ahh. English nerds like me (should be "like I") are fond of using the subjunctive and using "shall" and "will" properly. Almost NOBODY in the United States uses "shall" where it should be used. In Britain, the use of shall, correctly, is more frequent, but still not very frequent.