The authors study the hierarchy of properties that define lower bounded lattices within the class of all finite lattices. A lattice \(L\) is lower bounded if any homomorphism \(h\) from a finitely generated lattice \(K\) into \(L\) is lower bounded, i.e.\ if \(\{ x\in K\); \(a\leq h(x) \}\) is either empty or has a least element whenever \(a\in h(K)\). These properties are shown to be equivalent in the class of finite lattices, but not for infinite lattices. It is proved that an arbitrary lower bounded lattice is embeddable into an ultraproduct of finite lower bounded lattices. It follows that any lower bounded lattice defined by finitely many relations can be embedded into a direct product of the lattices of lower subsemilattices of the Boolean lattice \(2^n\) of all subsets of an \(n\)-element set. Several open problems are formulated.