Recently had an experience with misspelled first name. I made the booking by phone, and she typed a instead of e. Before the ticket issued at YVR airport, the agent tried to fixed my name so that matched with the name on my Senator card. But the first name could not be corrected. The good thing was that my Senator number accepted in the reservation. But to make sure everything allright, the agent put a note printed on my ticket stating the correct name. And I did not have any problem with that trip, and the miles had been credited properly.

I am sure, in your case Lufthansa will make a note regarding your first name.