  For a large class of time-dependent non-Hermitain Hamiltonians expressed in
terms linear and bilinear combinations of the generators for an Euclidean
Lie-algebra respecting different types of PT-symmetries, we find explicit
solutions to the time-dependent Dyson equation. A specific Hermitian model with
explicit time-dependence is analyzed further and shown to be quasi-exactly
solvable. Technically we constructed the Lewis-Riesenfeld invariants making
useof the metric picture, which is an equivalent alternative to the
Schr\"{o}dinger, Heisenberg and interaction picture containing the
time-dependence in the metric operator that relates the time-dependent
Hermitian Hamiltonian to a static non-Hermitian Hamiltonian.
