  In a recent preprint, Lai showed that the quotient of generating functions of
weighted lozenge tilings of two "half hexagons with lateral dents", which
differ only in width, factors nicely, and the same is true for the quotient of
generating functions of weighted lozenge tilings of two "quarter hexagons with
lateral dents". Lai achieved this by using "graphical condensation" (i.e.,
application of a certain Pfaffian identity to the weighted enumeration of
matchings).
  The purpose of this note is to exhibit how this can be done by the
Lindstr\"om--Gessel--Viennot method for nonintersecting lattice paths. For the
case of "half hexagons", basically the same observation, but restricted to mere
enumeration (i.e., all weights of lozenge tilings are equal to $1$), is
contained in a recent preprint of Condon.
