Whitman's condition in a lattice L means that, for any elements a, b, c, d ∈ L, a ∧ b ≤ c ∨ d implies either a ∧ b ≤ c or a ∧ b ≤ d, or a ≤ c ∨ d, or b ≤ c ∨ d. We prove that any lattice satisfying Whitman's condition can be embedded in the subgroup lattice of a free group of an arbitrary non-soluble group variety. Some interesting corollaries (both on embeddings in lattices of subgroups and others) are examined.