With apologies for bringing up an old thread, what you should be looking for is a 650mAh 803030 LiPo battery.
The six digit number is interesting because it seems to define the physical size of the battery, 30mm by 30mm by 8mm.
I’ve had a quick look on ebay and nobody seems to be selling that size battery. I suspect that Lezyne may have had their batteries custom made to that size, or they are buying them from every source possible.
The connector is a JST PHR-2, which is just the plastic part. You need to buy the crimps as well (JST PH 2mm female).
If the batteries were available, you could probably buy a battery with the right connector all ready to go.
Have you talked to your local dealer, or Lezyne yourself about having your light repaired (warranty or not)?