The magnetic ordering within LiMBO3 compounds (M = Mn, Fe, and Co) has been explored by magnetization measurements and neutron powder diffraction. For all M, an incommensurately ordered magnetic phase is established on cooling, followed by a change to a commensurate long-range antiferromagnetic state below TN2 = 12(1) K for LiMnBO3, TN2 = 25(1) K for LiFeBO3, and TN2 = 12(1) K for LiCoBO3. For LiMnBO3, the magnetic ordering at T = 2 K exhibits a propagation vector k = (1, 0, 0) and consists of antiferromagnetic chains that are coupled antiferromagnetically to each other, the magnetic moments being oriented along the [001] direction. In contrast, the magnetic order at T = 2 K in LiFeBO3 and LiCoBO3 exhibits a propagation vector of k = (1/2, 1/2, 1/2) and consists of ferromagnetic chains that are antiferromagnetically coupled. The magnetic moments lie roughly along the [023] direction within the bc plane for LiFeBO3, and along the [301] direction within the ac plane for LiCoBO3. The moment orientations in both LiMnBO3 and LiFeBO3 suggest an Ising character arising from unquenched orbital momentum due to unusual trigonal bipyrimidal coordination environments. No evidence of Ising behavior is found in the case of LiCoBO3.