So, you really couldn't use two lithium ions because that would be 7.4V and the aforementioned, POOF!, right? And you couldn't use one either, because the 3.7V would be below the min 4V, so no go. Guess BB750 and lithium-ion batts can't mix!
I had sucess on 2 123s. I'm told (here) that additional heatsinking is needed for the IC and diode on the BB 750. This means get some metal thermal-epoxied against them.
I know the LS would be ok with 7.4V, but won't using over 7V push the BB750 out of regulation? I thought there was a max and a min voltage window for the BB to operate.
The LS may or may not be okay with 7.4V. It totally depends upon the Vf characteristics of that particular LS. If you have a high enough Vf, then the LS will be fine with 7.4 V; but if you have a low Vf LS, then poof. (or at least _hot_)
I believe that the BB750 is fine as long as the input voltage is below the output voltage.