I'm also curious about their lifetime. My laptop batteries are pretty weak after three or four years. It's much easier to justify $thousands as a one-time purchase than $thousands/year. For many of its applications, this is going to have to beat a generator. Which, come to think of it, probably means that if they're pitching this as a way off the grid it is precisely because it won't be even remotely competitive with a generator.
You charge your laptop everyday. So it depends on how often you recharge them, which means it will depend on how big of a battery you'll buy. If you buy a 100 KWh battery (probably around $10,000-$15,000), I think that should last most Americans at least several nights to a week? So it might approach 10 years before it starts degrading, and then probably a few more years of charging it every day. I assume's Tesla's batteries will be relatively high-quality as well.
Isn't the idea that you keep it topped of and use it when grid power is expensive or missing? That usage pattern would involve multiple charge cycles, perhaps even 365 in a year. I guess it would actually follow the Tesla charging patterns fairly close as well. What is the estimated lifetime of a Tesla's battery?
If the battery has sufficient excess capacity, you can split it into multiple banks of smaller batteries, and cycle which ones you charge and which ones you use. Add a small computer and you can use whatever logic gives you optimal charging/discharge patterns to optimise for lifetime.
For a given generation of lithium battery cell and management technology, there is the option of trading off between capacity and durability.
Field-replaceable laptop batteries are engineered as a consumable, and runtime, weight and charging speed are given priority over long life. Laptops with integrated batteries make a somewhat different tradeoff, but still assume that battery replacement will be a maintenance expense for some users. In both cases, the expected average lifetime of the laptop itself is also a factor, which I'd guess would be about 5 years, max.
Packs for laptops make different tradeoffs vs packs for a car, or home power storage. From memory, based on some back of envelope calculations, tesla trades 15-20% of nominial capacity of the cells in their auto packs for >=4x or greater durability. Packs for home energy storage would probably make similar tradeoffs, and might get more life with less aggressive charging rates.