Why are lead-acid batteries preferable for submarines?
Unlike surface vessels, submarines have to be able to sink.  Every cubic foot of air space in a sub must be counterbalanced by almost 60 pounds of weight for a vessel to be able to submerge, and many submarines have a significant quantity of ballast for that purpose.  Lead acid batteries have much less energy per unit mass than lithium-based batteries, but their energy per unit volume is pretty respectable (nb: something seems a little odd with that Wikipedia table; lead acid batteries weigh so much more than LiIon per unit volume that the difference in volumetric energy density should be much less than the difference in mass energy density).  If one were to replace the batteries in a sub with magical batteries which stored the same energy and took up the same space, but weighed almost nothing, it would be necessary to add ballast to make up for the loss of weight (reducing the volume available for other purposes).  It may well be that on some diesel subs, the batteries weighed more than ideal, and thus the weight of batteries was a limiting factor (rather than volume), but nuclear subs have much smaller stored-battery-energy requirements than diesels.

Also, lead acid batteries have more of a proven history of not going up in flames than do lithium-ion batteries.  A submarine is not a good place to have things that may spectacularly catch fire.