First, you're missing something. Combining two lithium ions in series does not result in 7.2 V. If they are freshly charged, it results in 8.4 V.
Then as they are used and current is drawn out of them, they fall down to 6V, at which point they need to be recharged.
Next, you seem to be ignoring every reply these guys have offered you, not just in this thread but in all others. Out of curiosity, how old are you?
Finally, YES you can exchange the LM317 with LM1117 (half the voltage drop) but if you would have done any kind of search on your own, you'd know it already.