We investigate classical Heisenberg models on the distorted windmill lattice and discuss their applicability to the spin-1/2 spin liquid candidate PbCuTe2O6. We first consider a general Heisenberg model on this lattice with antiferromagnetic interactions Jn (n=1,2,3,4) up to fourth neighbors. Setting J1=J2 (as approximately realized in PbCuTe2O6) we map out the classical ground-state phase diagram in the remaining parameter space and identify a competition between J3 and J4 that opens up interesting magnetic scenarios. Particularly, these couplings tune the ground states from coplanar commensurate or non-coplanar incommensurate magnetically ordered states to highly degenerate ground-state manifolds with subextensive or extensive degeneracies. In the latter case, we uncover an unusual classical spin liquid defined on a lattice of corner-sharing octahedra. We then focus on the particular set of interaction parameters Jn that has previously been proposed for PbCuTe2O6 and investigate the system's incommensurate magnetic ground-state order and finite-temperature multistage ordering mechanism. We perform extensive finite-temperature simulations of the system's dynamical spin structure factor and compare it with published neutron scattering data for PbCuTe2O6 at low temperatures. Our results demonstrate that thermal fluctuations in the classical model can largely explain the signal distribution in the measured spin structure factor but we also identify distinct differences. Our investigations make use of a variety of different analytical and numerical approaches for classical spin systems, such as Luttinger-Tisza, classical Monte Carlo, iterative minimization, and molecular dynamics simulations.
