  We describe a family of indefinite theta functions of signature $(1,1)$ that
can be expressed in terms of trace functions of vertex algebras built from
cones in lattices. The family of indefinite theta functions considered has
interesting connections with mock theta functions and Appell-Lerch sums. We use
these relations to write the McKay-Thompson series of umbral moonshine at
lambency $\ell=8,12,16$ in terms of trace functions of vertex algebras modules,
and thereby provide the modules for these instances of umbral moonshine.
