Those figure certainly aren't true and accurate but are just estimates, so we can only really talk in vague terms about them.
AIP has its moments going slow. AFAIK no one is underwater for 60 days using AIP. Its usually more like 21 days as claimed by manufacturers, even at slow speeds. Then there are questions. At what temperature? Tropical waters? Arctic waters? At maximum depth? How reliable? Are there limitations that will affect operations?
To my knowledge, there are no known battery improvements in the "R&D pipeline" any where in the world, that can come close to fill such a gap.
It doesn't have to, it gets back to CONOPs. I would think it would be rare even for SSN's to remain completely submerged at depth for 60 days.
Lithium batteries aren't just about increasing storage density. Lithium key advantage over lead acid is really when you want to put a lot of current in and take a lot of current out. Combined with supercapacitors, you can surge huge amounts of energy (in or out) without the penalty of lead acid. Lithium potentially makes your indiscretion more effective. You can charge quicker, have less issues from your batteries. While fuel cell AIP is quiet, lithium ion is even quieter. Fuel cell AIP supplies small amounts of power, lithium solutions can surge significantly more.
Both the French and German proposals see lithium as adding to the party rather than replacing fuel cells. The Japanese did replace a rather dated (hence my 1980's or should that be 1880's) Kockums sourced Stirling AIP system directly with lithium ion, so it could potentially make that difference, even for very deep diving subs like the Japanese. For them, its worth it.
I don't see diesel engines disappearing completely in the near/medium term. Its about complimenting them. Making them more efficient and capable. Diesel engines are cheap to buy and operate, diesel is cheap and is a dense energy source. Even nuclear submarines have diesel engines as backups. Nuclear submarines still have periscopes, they still approach the surface for a large number of reasons.
I think AIP systems will still be a part of submarines for a while yet, but I think subs will be less and less designed around them. Everyone wants to get away from carrying hydrogen which is stored at low density and is generally problematic. Ideally you could make your own hydrogen from diesel fuel using a reformer, but making enough efficiently with regular diesel is space consuming. Liquid oxygen needs to be kept cool obviously. Long transits through tropical water do not seem like ideal situations for any AIP that uses liquid oxygen.
For many navies, AIP doesn't really deliver for the CONOPs. Japan has pretty extensive fuel cell capabilities, with Toyota, Honda and other manufacturing fuel cell cars, industrial equipment etc so its not like the technology is beyond them. But they have migrated directly to lithium ion as the replacement for its AIP.
The latest MESMA system is alleged to power at sub at 6kts while having excess available for charging batteries (or allowing greater than 6kt performance), and can reform fuel from diesel. TKMS is also looking at reforming from methanol, the spanish do reform from Methanol.
TKMS has proposed a system to replenish liquid oxygen at sea, allowing it to be replenished during snorting.
So in design terms, I think it would be worth while allocating space/weight for AIP, and some sort of liquid oxygen storage. AIP is likely to become more compact over all. Enhancing capabilities rather than being the magical do everything power source of the future.
Lithium ion in subs is likely to be part of a wide system. GF who is much more aware and informed than I, indicates supercapacitors are part of that solution, further amplifying their strengths. I think between them they can offer huge benefits in many applications. They would be paired with a complex battery management system to squeeze the most out of the different types of energy systems on a sub.
Which is then the key part, trying to integrate and make the most of the technologies now available.