  In this article we study proper symplectic and iso-symplectic embeddings of
$4$--manifolds in $6$--manifolds. We show that a closed orientable smooth
$4$--manifold admitting a Lefschetz fibration over $\C P^1$ admits a symplectic
embedding in the symplectic manifold $(\C P^1 \times \C P^1 \times \C P^1,
\omega_{pr}),$ where $\omega_{pr}$ is the product symplectic form on $\C P^1
\times \C P^1 \times \C P^1.$ We also show that there exists a sub-critical
Weinstein $6$--manifold in which all finite type Weinstein $4$--manifolds admit
iso-symplectic embeddings.
