DMCA notices -- by which, presumably, you mean takedown notices -- are only required to a third-party that is otherwise within the DMCA safe harbor protecting hosts of allegedly-copyright-infringing user-submitted content to choose either to take the content down or forfeit the protection of the safe harbor. They have nothing to do with actions against direct violators of either the main body of copyright law or the anti-circumvention provisions of the DMCA.
> I persume they can't file a lawsuit without filing DMCA takedown notice first?
You presume incorrectly; even if the alleged violation was of the type to which a DMCA takedown was relevant, they can sue the offending party (though not a third-party host within the safe harbor) without a takedown notice.
I persume they can't file a lawsuit without filing DMCA takedown notice first?
If so, when they'll file the notice, GitHub'll take it down (as they usually do). Then you may consider filing counter-notice (if you can afford legal action) or, I guess (IMNAL!) ignore the whole affair.
Anyway, you'd better consult a lawyer.