  The origin of the astrophysical high-energy neutrinos discovered by IceCube
is currently a major mystery. The recent detection of IceCube-170922A, a
$\sim$300 TeV neutrino potentially correlated with the flaring $\gamma$-ray
source TXS 0506+056, directs attention toward BL Lac objects (BL Lacs), the
subclass of blazars with weak emission lines. While high-energy neutrinos can
be produced via photohadronic interactions between protons accelerated in their
jets and ambient low-energy photons, the density of the latter in such objects
had generally been thought to be too low for efficient neutrino emission. Here
we consider the role of radiatively inefficient accretion flows (RIAFs), which
can plausibly exist in the nuclei of BL Lacs, as the source of target photons
for neutrino production. Based on simple model prescriptions for the spectra of
RIAFs at different accretion rates, we find that they can be sufficienly
intense to allow appreciable neutrino emission for the class of
low-synchrotron-peak BL Lacs such as TXS 0506+056. In constrast, for
high-synchrotron-peak BL Lacs including Mkn 421 and Mkn 501, the contribution
of RIAFs is subdominant and their neutrino production efficiency can remain
low, consistent with their non-detection by IceCube to date.
