  In recent work, M. Just and the second author defined a class of
"semi-modular forms" on $\mathbb C$, in analogy with classical modular forms,
that are "half modular" in a particular sense; and constructed families of such
functions as Eisenstein-like series using symmetries related to integer
partitions. Looking for further natural examples of semi-modular behavior, here
we construct a family of Eisenstein-like series to produce semi-modular forms,
using symmetries related to Fibonacci numbers instead of partitions. We then
consider other Lucas sequences that yield semi-modular forms.
