There’s been a lot of discussion about lithium batteries on ukgser. A lot of people are big fans of them as they hold their charge for a long time. This is, as far as I can see, their biggest and main advantage. The other is weight saving, although hardly worth it on a 250kg bike. If you use the bike regularly enough to keep the battery charged or can put a battery charger on it then I personally don’t think they are worth it.
The cold start thing apparently is helped by letting the battery discharge a little before hitting the starter, eg a light on for a minute or two, this starts the chemical processes in the battery and warms it internally. More cold cranking amps magically then become available it seems.