When the cells swell up like that, they have usually overcharged or overdischarged or had some other internal failure, and are damaged, and would need to be replaced.
If the battery sat unused for months with the BMS attached, it's possible the power needed to run the BMS drained the pack below usability. (if it was left attached to the bike or any other load, the load could have drained it, even if the device was "off" if it isn't an off switch that actually physically disconnects the battery from the load).
As for what to replace it with...if it only sees a little use every so often, get or make a pack that you can completely physically disconnect the BMS from, or ensure you test the battery and recharge at least partially as often as necessary while not in use.
There are various storage protocols discussed in many threads around the forum, most of which recommend leaving the battery at 50% or less amount of charge, to lower the stress on the cells (increase lifespan). But if you have a BMS or other load on the battery, the drain from it may kill the battery in the time it sits there if you don't monitor it.
Lead would be the worst choice, as it will self-discharge even if not connected to anything. (well, everything self-discharges but lead is pretty bad about it). Also, lead will be damaged (sulfated) by not being at it's full-charge state.