I'd be interested in this answer, as I asked the same question a few weeks back when it was still called the G+ plugin:
Same issues here (I just popped over to report and saw this thread). The Livefyre integration works great, but then the issue of new post and double comment boxes appears. I've dropped in three links here to screenshots.
1. This is a brand new post just published, and double comment box (with Livefyre also active):
2. This is the same post, with G+ active and Livefyre disabled on new posts:
3. And this is the old post from Sunday with G+ active and Livefyre disabled:
It seems to be posts published before activation of the G+ plugin with Livefyre support lose their comment box.
Any ideas? Thanks!