Note that FIPS 181 is from 1993, which is ancient, in computer security terms, and I doubt that NIST is actively recommending it, especially since as you say it only includes lower-case ASCII letters, making the passwords much easier to crack.
At a deeper level, since the goal is for passwords to be unpredictable, it is not generally good to promulgate a standard which would simply serve to restrict the set of possible passwords. That would make the attacker's job easier.
I recommend incorporating random inputs into your thinking when making a password, but then tweaking it in your own way to make it even less predictable. The apg program looks like what you're looking for, and is suitable for that kind of use, since it is easy to tweak the parameters, and to then tweak its suggestions. It refers to FIPS 181, but actually by default generates passwords that include symbols, digits and capital letters as well as lower case letters, and which can either be limited to more pronounceable ones or not.
The first thing you'll probably want to tweak (depending on your threat model) is to use the -m option to increase the minimum length to at least 12 characters so there is enough entropy in them. See entropy of FIPS-181 automated password generator - Information Security Stack Exchange for some background on the entropy of such passwords.
Note that I don't recommend using any of the many web pages that generate passwords using apg or the like - that's just asking for someone to remember (or spy on) all the ones that are handed out and add them to their cracking dictionary. Evidently that wasn't clear way back in 1986 to the authors of RFC 972 - Password Generator Protocol, which amazingly still lives on in my /etc/services file....
See also RFC 4086 - Randomness Requirements for Security