Will a lithium-ion battery powered lawn mower recharge after sitting idle though the winter?
Lithium batteries are not lead-acid.  They don't have all those &quot;bad habits&quot; like decaying when left in storage.
Tiny palm-sized packs such as for power tools do tend to age like normal power-tool packs and only give you 3-5 years life... but I understand lawnmower packs are bigger.
This assumes you buy quality and not some cheapo piece o' junk off Amazon Marketplace.
However, I gather you have apprehension about large lithium packs.  Lithiums do have certain rules.

Do not discharge them literally to zero.  Now, any competent lithium battery will have a Battery Management System (BMS) to protect the battery from a variety of things (including overcharge)... and it will disconnect the battery and shut down your appliance to protect it from too-deep discharge.   That does nothing about self-discharge from long storage, and I'd suggest putting them on charger every couple of months to keep them from reaching zero.
Do not recharge them if temp is below freezing.   In fact, if you try to recharge a Tesla whose battery has deep-frozen, it will first heat and circulate battery coolant, before it attempts to charge.
Never, ever, feed them after midnight.  Just kidding!


As far as buying 2 battery packs, if the supplied battery pack lacks the range to cut the whole lawn, just put the battery back on charger and cut the rest of it later.
Lithiums are happiest working in their midrange: 20-80%.  Charging is fastest and it does not need to be tapered/limited, like it must for 0-20% and 80-100%.  That's the trick about crossing the country in an EV: you can DC fast-charge within that 20-80% range very quickly.
So if it doesn't have range for the full lawn, stop at halfway and recharge... that way you'll be recharging from 20-50% SOC and it will charge pretty fast up to 80%.... then finish.