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We report on the ESR, magnetization and magnetic susceptibility measurements performed over a large temperature range, from 1.5 to 750 K, on high-quality stoichiometric LiNiO2. We find that this compound displays two distinct temperature regions where its magnetic behavior is anomalous. With the help of a statistical model based on the Kugel'-Khomskii Hamiltonian, we show that below T of ≃ 400 K, an orbitally-frustrated state characteristic of the triangular lattice is established. This then gives a solution to the long-standing controversial problem of the magnetic behavior in LiNiO2.