A linear lighting device with light-emitting diodes comprising at least: - an elongated body comprising at least one surface for receiving at least one substrate bearing a linear light source comprising at least one row (Rg) of light-emitting diodes aligned along a longitudinal axis of the body and delimiting, at least in part, at least one elongated linear lighting chamber in which the diodes are located, - an elongated linear lid closing the fighting chamber, characterized in that the lid forms, in relation with the linear source, a linear lens, at least translucent, of longitudinal axis parallel to the longitudinal axis of the body, with an external light emitting face and an inner light receiving face for emitting and receiving the light of the diodes, the emitting face having, in cross-section, a convex shape, and the receiving face comprising, in cross-section: - an offset convex medial dioptre that defines with the external face a biconvex medial lens whose optical axis is laterally offset with respect to a sagittal plane, - on one side of the medial dioptre, a first lateral prism that is adjacent to the medial dioptre, - on the other side of the medial dioptre, a series of prisms parallel to the first prism that comprises at least one second lateral prism and one third lateral prism, the second lateral prism being adjacent to the medial dioptre and to the third lateral prism, each lateral prism having a medial face and a lateral face at least in part planar, connecting with each other at a corresponding apex of the prism, the lateral prisms each having a height, measured between the apex of the corresponding prism and the external face, the height (H 2) of the second lateral prism being higher than or equal to the thickness (e) of the medial lens, measured between the apex of the medial dioptre and the external face. - an elongated body comprising at least one surface for receiving at least one substrate bearing a linear light source comprising at least one row (Rg) of light-emitting diodes aligned along a longitudinal axis of the body and delimiting, at least in part, at least one elongated linear lighting chamber in which the diodes are located, - an elongated linear lid closing the fighting chamber, characterized in that the lid forms, in relation with the linear source, a linear lens, at least translucent, of longitudinal axis parallel to the longitudinal axis of the body, with an external light emitting face and an inner light receiving face for emitting and receiving the light of the diodes, the emitting face having, in cross-section, a convex shape, and the receiving face comprising, in cross-section: - an offset convex medial dioptre that defines with the external face a biconvex medial lens whose optical axis is laterally offset with respect to a sagittal plane, - on one side of the medial dioptre, a first lateral prism that is adjacent to the medial dioptre, - on the other side of the medial dioptre, a series of prisms parallel to the first prism that comprises at least one second lateral prism and one third lateral prism, the second lateral prism being adjacent to the medial dioptre and to the third lateral prism, each lateral prism having a medial face and a lateral face at least in part planar, connecting with each other at a corresponding apex of the prism, the lateral prisms each having a height, measured between the apex of the corresponding prism and the external face, the height (H 2) of the second lateral prism being higher than or equal to the thickness (e) of the medial lens, measured between the apex of the medial dioptre and the external face. - an offset convex medial dioptre that defines with the external face a biconvex medial lens whose optical axis is laterally offset with respect to a sagittal plane, - on one side of the medial dioptre, a first lateral prism that is adjacent to the medial dioptre, - on the other side of the medial dioptre, a series of prisms parallel to the first prism that comprises at least one second lateral prism and one third lateral prism, the second lateral prism being adjacent to the medial dioptre and to the third lateral prism,