We report herein on the magnetic properties and structures of orthorhombic Li2M(SO4)(2) (M = Co, Fe) and their oxidized phases LixFe(SO4)(2) (x = 1, 1.5), which were previously studied as potential cathode materials for Li-ion batteries. The particular structure of these orthorhombic compounds (space group Pbca) consists of a three-dimensional network of isolated MO6 octahedra enabling solely super-super-exchange interactions between transition metals. We studied the magnetic properties of these phases via temperature-dependent susceptibility measurements and applied neutron powder diffraction experiments to solve their magnetic structures. All compounds present an antiferromagnetic long-range ordering of the magnetic spins below their Neel temperature. Their magnetic structures are collinear and follow a spin sequence (+ + - - - - + +), with the time reversal associated with the inversion center, a characteristic necessary for a linear magneto-electric effect. We found that the orientation of the magnetic moments varies with the nature of M. While Li2Co(SO4)(2) and Li1Fe(SO4)(2) adopt the magnetic space group Pb'c'a', the magnetic space group for Li2Fe(SO4)(2) and Li1.5Fe(SO4)(2) is P112(1)'/a, which might hint for a possible monoclinic distortion of their nuclear structure. Moreover we compared the orthorhombic phases to their monoclinic counterparts as well as to the isostructural orthorhombic Li2Ni(SO4)(2) compound. Finally, we show that this possible magneto- electric feature is driven by the topology of the magnetic interactions