48v 20 ah is just heavy enough to blow the seams on many of the soft lunchboxes. Some of the more stout offerings are more like 12 pack coolers, and tend to be too big.
I'd say the starting point would be to build a sturdy wood or metal shelf on the frame to support that weight, then figure out the bag. The bag is not supporting the weight that way so much.
For me, once you have a shelf on the frame, the logical step is to use 1/8" plate aluminum to make sides for the battery box. I like hard shells on my batteries. One reason I like the 36v 20 and 48v 15 ah size is they fit perfect in antique metal toolboxes.
If you do go the bag route, I highly recomend coroplast real estate or political sign material for crash protection. More abrasion resistant than foam. I've also made protective inner boxes out of cookie sheets and the top from a large storage tote. Even inside the metal box, I still have an inner liner that fits perfect on the batteries to completely eliminate chafing or dings on the cells.
Protect your battery well. Mine have been through some wild crashes, leaving the bike when racks broke, etc with no physical harm to any of my batteries. Nothing is funnier to me than the guy who says, " I've made sure nothing can happen" It happens anyway eventually.
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.