One of my group members did not contribute anything and I notified my course lecturer. Did I do the right thing?
No, you didn't do the wrong thing. She did not notify you in advance of the deadline, and you needed to submit to avoid incurring your own penalties. She and the instructor can sort out the mark - it may be that her issues meet the guidelines for special consideration for example. Ultimately, it's none of your business and not your responsibility.

I know some instructors think that group work is a good way of preparing for teamwork in the real world. But, in the real world, problems like this are handled by the boss, not the other team members. On the other hand, you should learn from the experience to have all the team members commit to completing their pieces in advance of the deadline (preferably a week or so in advance if there's enough time), so that you have a chance to resolve such problems before the project completion date.