4 pages, 5 figuresSusceptibility, high-field magnetization and submillimeter wave electron spin resonance measurements of layered quasi-stoichiometric Li1-xNi1+xO2 are reported and compared to isomorphic NaNiO2. A new mechanism of magnetic frustration induced by the excess Ni ions always present in the Li layers is proposed. We finally comment on the possible realization of an orbital liquid state in this controversial compound