The only thing I haven't been able to find is exactly how I could connect the lithium batteries to the empeg,

You're making things more complicated and expensive than they need to be.

You don't need a lithium-ion battery. Save yourself $100 or so, and just get a 12 Volt lead acid gel-cell battery, the type used for emergency lighting systems and burglar alarms. A small six amp-hour battery will set you back about $25, and will run the empeg for about 8 hours without deep-cycling. A small automotive charger will re-charge it, cost you about $20. Radio Shack will sell you a plug that plugs right into the empeg for about $2. And they'll sell you the matching plug to put on the charger for the same price. Leave the charger plugged into the wall all the time, and just unplug the battery from the empeg and into the charger to recharge. Whole setup will cost about $50 and weigh about six pounds.

This is how I installed my empeg on my bicycle for when I commute to work. See here

tanstaafl.