Recent multiwavelength work led by the Boston University blazar group (e.g., Marscher et al. 2010) strongly suggests that a fraction of the blazar flares seen by the Fermi Large Area Telescope (LAT) take place a few to several pc away from the central engine. However, at such distances from the central engine, there is no adequate external photon field to provide the seed photons required for producing the observed GeV emission under leptonic inverse Compton (IC) models. A possible solution is a spine-sheath geometry for the emitting region (MacDonald et al. 2015, but see Nalewajko et al. 2014). Here we use the current view of the molecular torus (e.g., Elitzur, 2012;Netzer 2015) in which the torus extends a few pc beyond the dust sublimation radius with dust clouds distributed with a declining density for decreasing polar angle. We show that for a spine-sheath blazar jet embedded in the torus, the wide beaming pattern of the synchrotron radiation of the relatively slow sheath will heat molecular clouds whose subsequent IR radiation will be seen highly boosted in the spine comoving frame, and that under reasonable conditions this photon field can dominate over the sheath photons directly entering the spine. If the sheath is sufficiently luminous it will sublimate the dust, and if the sheath synchrotron radiation extends to optical-UV energies (as may happen during flares), this will illuminate the sublimated dust clouds to produce emission lines that will vary in unison with the optical-UV continuum, as has been very recently reported for blazar CTA 102 (Jorstad et al. 2017).