Organic lithium battery comprising: - a negative electrode comprising lithium metal or an alloy of lithium metal, - a positive electrode optionally supported by a current collector, said positive electrode comprising at least one redox organic structure comprising at least two carbonyl C=O functional groups, two thione C=S functional groups or two imine C=N functional groups, at least one polymer binder P 1 and at least one agent generating electron conductivity, said redox organic structure being different from the sulphur-comprising agents chosen from elemental sulphur S 8 and sulphur-comprising organic compounds comprising at least one S-S bond, said organic lithium battery being characterized in that it additionally comprises an electrolyte comprising at least one lithium salt L 1 and at least one liquid linear or cyclic polyether with a molar mass of less than or equal to 10 000 g·mol -1, it being understood that: * when the electrolyte is a liquid electrolyte, the concentration of lithium salt L 1 in said liquid electrolyte is at least 1.6 mol/l, and the liquid electrolyte impregnates a porous separator, and * when the electrolyte is a gelled polymer electrolyte, it additionally comprises at least one polymer binder P 2 which is soluble in the liquid linear or cyclic polyether with a molar mass of less than or equal to 10 000 g·mol -1, and the concentration of lithium salt L 1 in said gelled polymer electrolyte is such that the O/Li ratio is at most 15, it being understood that, in the O/Li ratio, "O" denotes the number of oxygen atoms provided by the ether units of the liquid linear or cyclic polyether with a molar mass of less than or equal to 10 000 g·mol -1, and optionally by the ether units of the polymer binder P 2, if it contains them, and "Li" denotes the number of lithium ions provided by the lithium salt L 1. - a negative electrode comprising lithium metal or an alloy of lithium metal, - a positive electrode optionally supported by a current collector, said positive electrode comprising at least one redox organic structure comprising at least two carbonyl C=O functional groups, two thione C=S functional groups or two imine C=N functional groups, at least one polymer binder P 1 and at least one agent generating electron conductivity, said redox organic structure being different from the sulphur-comprising agents chosen from elemental sulphur S 8 and sulphur-comprising organic compounds comprising at least one S-S bond, * when the electrolyte is a liquid electrolyte, the concentration of lithium salt L 1 in said liquid electrolyte is at least 1.6 mol/l, and the liquid electrolyte impregnates a porous separator, and * when the electrolyte is a gelled polymer electrolyte, it additionally comprises at least one polymer binder P 2 which is soluble in the liquid linear or cyclic polyether with a molar mass of less than or equal to 10 000 g·mol -1, and the concentration of lithium salt L 1 in said gelled polymer electrolyte is such that the O/Li ratio is at most 15, it being understood that, in the O/Li ratio, "O" denotes the number of oxygen atoms provided by the ether units of the liquid linear or cyclic polyether with a molar mass of less than or equal to 10 000 g·mol -1, and optionally by the ether units of the polymer binder P 2, if it contains them, and "Li" denotes the number of lithium ions provided by the lithium salt L 1.