Thicker neoprene would be ideal, 1/8 is fairly thin. Wetsuits can be cheap at goodwill or similar stores.
Another good material I use inside my battery boxes is 1/4 inch thick neoprene like closed cell foam. Get it by buying a yoga mat. Again, goodwill for it cheap.
If you have 1/2 inch of space to take up, then the cheap closed cell foam anti fatigue/playground mats are great, or a closed cell camping pad for sleeping.
But really, if you have a good box, that's your main protection. Chafing and puncture are the main hazards, and the box prevents puncture. So fit em in nice and snug using anything to prevent chafing and excess movement, cardboard, shipping foam sheets, whatever. Just have the pack rub on soft anything, rather than a screw head or such.
THE LIPO RULES. NEVER ABOVE 4.3V NEVER BELOW 2.7V DON'T PUNCTURE
Ideal charging /discharging range for Lipo, 3.65v minimum 4.1v maximum
See battery technology section, FAQ thread at the top of the page for lipo noob info.