  We treat the almost differentiable left A-loops as images of global
differentiable sharply transitive sections $\sigma :G/H \to G$ for a Lie group
$G$ such that $G/H$ is a reductive homogeneous manifold. In this paper we
classify all $3$-dimensional connected strongly left alternative almost
differentiable left A-loops $L$, such that for the corresponding section
$\sigma :G/H \to G$ the Lie group $G$ is non-solvable.
