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It is known that every atomic ortho-modularlattice is also atomistic. Is the converse also true?

If not, can someone give me some examples of atomistic ortholattices which are not modular?

By atomistic I mean that the lattice has atoms and moreover, every element of the lattice can be expressed as a join of atoms.

Let $L$ be an atomic ortholattice. We say that two elements $a$ and $b$ of $L$ are orthogonal if $a\leq b^\perp$. If $L$ is orthomodular then every element of $L$ can be written as a join of pairwise orthogonal atoms of $L$. Is the converse also true?