Lately, there had been keen explorations into a new type of novel waveguide that enjoys, over a wide bandwidth, the desirable trait of having only one TEM mode propagating along just the direction of a metallic rectangular ridge embossed onto a wall of a parallel-plate waveguide and existing only within the resultant ridge-gap, achieved by a textured high-impedance surface surrounding the ridge which suppresses the propagation of global TEM modes along all other directions. Referred to as gap-waveguides , a typical bandgap structure that has been used is the so-called bed-of-nails comprising simply an array of grounded metallic pins . Motivated by the broadband nature of such high-impedance surfaces, it could hence also be interesting and worthwhile to investigate how such a pin-lattice, when implanted within the sidewall dielectric slab-loadings of a rectangular waveguide, could affect the bandgap properties. An asymptotic treatment of this pin-lattice loaded waveguide is proposed, through the use of classical analysis by vector potentials and assuming a "TEM-to-slab-surface-normal" solution inside the pin-lattice layer. Hence, the approach is plausible only within the premise of diminishingly small pin-periods, i.e. the spatial density of the pins tends to infinity. Nevertheless, this method provides extremely rapid analysis processes as compared to full-wave solvers, which is vital for design and optimization procedures.