  We propose a conjecture regarding the integrally closedness of lattice
polytopes with large lattice lengths. We demonstrate that a lattice simplex in
dimension 3 (resp. 4) with lattice length of at least 2 (resp. 3 and no edge
has lattice length 5) can be covered by dilated simplices of the form $sQ$,
where integer $s\ge 2$ (resp. 3) and $Q$ is a lattice simplex. The covering
property implies these simplices are integrally closed. As an application, we
derive a simple criterion for the projective normality of ample line bundles on
weighted projective spaces of dimension 3 (resp. 4). Along the way, we discover
certain unexpected phenomenon.
