  We present techniques, inspired by monodromy considerations, for constructing
compact monotone Lagrangians in certain affine hypersurfaces, chiefly of
Brieskorn-Pham type. We focus on dimensions 2 and 3, though the constructions
generalise to higher ones. The techniques give significant latitude in
controlling the homology class, Maslov class and monotonicity constant of the
Lagrangian, and a range of possible diffeomorphism types; they are also
explicit enough to be amenable to calculations of pseudo-holomorphic curve
invariants.
  Applications include infinite families of monotone Lagrangian $S^1 \times
\Sigma_g$ in $\mathbb{C}^3$, distinguished by soft invariants for any genus $g
\geq 2$; and, for fixed soft invariants, a range of infinite families of
Lagrangians in Brieskorn-Pham hypersurfaces. These are generally distinct up to
Hamiltonian isotopy. In specific cases, we also set up well-defined counts of
Maslov zero holomorphic annuli, which distinguish the Lagrangians up to
compactly supported symplectomorphisms. Inter alia, these give families of
exact monotone Lagrangian tori which are related neither by geometric mutation
nor by compactly supported symplectomorphisms.
