Mathworker21's definition is probably what's intended, and you are correct about a connection to dynamical systems. However, nilsystems are always zero entropy, and $\lambda_n(f)$ is (I assume) conjectured to have positive entropy. If so, the associated dynamical system will probably have a Bernoulli factor - see Theorem 1.6 of of this article by Frantzikinakis and Host for explicit examples of constructing and analyzing systems associated to number theoretic sequences.