Here's a description of that bike when it was new: http://www.electricbikes500.com/electric-sierra.html
It uses SLA (sealed lead acid) batteries, which are relatively cheap and easy to obtain, such as at a BatteriesPlus outlet store. You'd need to take in the exact batteries you pull from the bike's case. It will require two 12-volt batteries.
"Volts are volts" is a true statement, as far as it goes, but batteries and controllers differ in the maximum amount of current (amps) or power (watts) they can handle or produce. You need to match them up with each other's specs. BatteriesPlus probably has an exact replacement. I did exactly that when I replaced the two 12-volt batteries from my EVG eBike a few years ago, and the replacements worked fine.
One note of caution. My eBike had such dead batteries that they crystlized and cracked their cases inside the battery pack's outer case. I had a heck of a time getting them out because they had swollen and the heat they generated had fused the plastic cases. Also, the posting her which suggested that maybe more is wrong than just the dead batteries should be considered.
I heard that the manufacturer of the Synergy bikes closed his store in Santa Cruz and moved to Pacific Grove, California. Just an unconfirmed rumor. You may be able to find him for further advice.