It's an interesting question. For military applications, I believe the answer may be considered a secret since it has implications on the performance and range of a sub. There are definitely manufacturers of li-ion submarine batteries and with fewer exemptions from RoHS etc for military applications, increases in performance and safety of li-ion, there are fewer reasons to go lead-acid. I believe the Japanese have announced the use of li-ion in some subs.
The submarine "industry" closer to home is however very, very conservative and the programme life can be upward of 80 years which puts constraints on the availability of supply, dependency on other nations that produce sufficient quantities of lithium and a need to stockpile spares, all of which make lead-acid more favourable. I would imagine that there is a certain amount of flexibility designed into the system for both diesel-electric and nuclear subs such that some of the risks can be mitigated and an alternative battery technology be changed in during the 10- or 20-year refits.
Hope that's something to go on, but I don't think it's an exclusive yes or no answer across the board.