Magnetic structures are investigated by means of neutron diffraction to shine a light on the intricate details that are believed to be key to understanding the magnetoelectric effect in LiCoPO4. At zero field, a spontaneous spin canting of φ=7(1)∘ is found. The spins tilt away from the easy b-axis toward c. Symmetry considerations lead to the magnetic point group m′z, which is consistent with the previously observed magnetoelectric tensor form and weak ferromagnetic moment along b. For magnetic fields applied along a, the induced ferromagnetic moment couples via the Dzyaloshinskii-Moriya interaction to yield an additional field-induced spin canting. An upper limit to the size of the interaction is estimated from the canting angle.