The lead-acid 12V auxiliary batteries are still a common thing in modern electric vehicles, despite the traction batteries are, in almost all cases, some kind of lithium-ion chemistry.
That's probably because they are "good enough" for the purpose, less expensive and there were tons of other higher-priority areas to improve efficiency to even bother with 12V lithium batteries.
Only rarely did we see new high-end sports models to go with lithium-ion (to save some weight) or third-party solutions for do-it-yourself replacement.
Most recently, however, Tesla's Elon Musk announced that the new, refreshed Model S/Model X will be factory-equipped with a lithium-ion 12V auxiliary battery. That should eliminate some weakness of the lead-acid battery (calendar-life, reliability, weight, size, increase capacity), and they are more suited for the application of EVs (no high-amperage cranking like an internal combustion engine application).
The only downside of the lithium-ion battery is the price, but the total cost of ownership might be similar or lower (especially if you can avoid the problem of dead 12V and a necessity of emergency replacement at some point down the road).
Some of the EV owners might consider replacing the lead-acid 12V battery with lithium-ion on their own using third-party solutions.
In the Annies Carparts' video above, we can see an example of that, using a Liontron battery (12.8 V / 20 Ah nominal, which is about 256 Wh) for a Tesla Model X. The price of such battery is around €250 we believe ($300), there are also other versions from 10.5 Ah up to 200 Ah.
A cool thing about this particular solution is the battery management system (BMS) with integrated Bluetooth interface and Android or Apple iOS app to check the battery status from time to time.
Is it worth it to switch to lithium-ion on its own? Well, if there is no warranty and the lead-acid is on its last legs, some will probably give it a try.
And here is the manufacturer video, showing what is inside (English subtitles):