Sure, a business can cease to operate—that's a risk that seems pretty clear cut and understandable. Or, if the business completely changes and doesn't offer that type of product or service anymore. If the lifetime offer was for unlimited (one at a time) VHS borrowing at the neighborhood video rental, and then the store shifted to only offering DVDs, or (perhaps better) streaming, the fact that there are no longer any VHS tapes to borrow makes sense.

But this is a case of an email company (likely profitable) that still offers email accounts. It's likely that the only difference between the product that they're taking away and current offerings is that the 'lifetime' accounts have FAR lower quotas and features offered. The cost of computing, storage and bandwidth trend downward over time. No new lifetime accounts are being created, so they've got a fixed quantity of lower-usage level accounts. They can already forecast the maximum technical cost for these over the next 10/20/30/40 years. Now these accounts may have high costs in terms of providing customer support, and that would be unpredictable, and potentially costly. I doubt anyone would fault Fastmail for simply stating that outside of a few designated problems/issues (either on their side or the most important) that no technical support would be provided for these accounts. If they wanted to be nice, they might offer that non-crucial support issues could be handled at the lowest tier/priority.

That would be a sensible way to move forward.