We investigate the complexity of the lattice of local clones over a countably
infinite base set. In particular, we prove that this lattice contains all
algebraic lattices with at most countably many compact elements as complete
sublattices, but that the class of lattices embeddable into the local clone
lattice is strictly larger than that: For example, the lattice $M_{2^\omega}$
is a sublattice of the local clone lattice.