Short answer: Almost certainly yes -- but double check with the check-in agent and then double check the final destination on the baggage stub you get. Longer answer follows.
If you booked both tickets together then definitely yes, it'll be booked as a single journey and your luggage will go to Boston as there's no policy requiring you to recheck luggage in Frankfurt (or inside the EU, that I know about). The only case were you might have to recheck the luggage is on a very long stopover (longer than 24 hours) some airports will not let you do this, but I suspect this is not the case for you.
If you've booked the tickets separately then you'll need to make clear to the agent on the check-in desk that you want the bag checked all the way, and show your passes. As long as the details match on both tickets they should do this. Now, I've had to insist that they do this in the past because their first position might be to say it's impossible, but it's not and they definitely can do it. That was on KLM but Lufthansa should be similar.
If you want backup, and you have separate tickets, contact customer services (contact details) and explain to them.