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We demonstrate that the phase diagram of a Lyotropic Chromonic Liquid Crystal (LCLC) is affected by ultraviolet (UV) light irradiation. UV-irradiation induces a phase transition from the nematic (N) to isotropic (I) state at a fixed temperature. Birefringence measured in-situ decreases under irradiation, until the moment when the isotropic phase starts to nucleate and the initial homogeneous nematic transforms into a biphasic state. On further irradiation the birefringence of the N fraction of the biphasic I-N state increases revealing redistribution of the composition components between the two coexisting phases. The efficiency of the irradiation-induced changes depends on the orientation of the chromonic aggregates w.r.t. the polarization of UV light. Changes of the birefringence are noticeably higher for light polarization perpendicular to the nematic director. The effect can be understood as a photo-induced weakening of the face-to-face molecular attraction within the chromonic aggregates and the resulting shortening of these aggregates.