Rota is not around anymore, so we can't go and ask him what he meant. My guess is that he is referring to the $\lambda$-ring structure of symmetric functions which is related to plethysm and the composition of Schur functors (that's the representation theory connection as well as the category theoretic one regarding polynomial functors). This $\lambda$-ring structure plays a role in $K$-theory as explained, e.g. see "Riemann-Roch Algebra" by Fulton and Lang. For other references see, e.g,
- This set of notes by Darij Grinberg.
- Donald Yau's "Lambda-Rings" book
- This survey article about big Witt vectors by Hazewinkel.