Quantum-mechanical effects of incorporation of the Cu ions at the Li sites in Li2B4O7 crystal matrix are investigated by means of first-principles calculations on density-functional-theory level. The isolated Cu defect is considered in various charge states with objective to simulate situations of the capture of an electron or a hole. In all cases the defective crystal is computationally relaxed, Cu-O chemical bonds carefully analyzed and local structure around the defects precisely determined. It is found that the defect vastly perturbs its O neighborhood and the Cu itself exhibits significant off-site dislocation from initial Li position in its Cu1+ and Cu0 charge states, while the Cu2+ stabilizes approximately at the Li site. Resulting defect formation energies demonstrate that the Cu1+ and Cu0 centers are the most stable ones. Electronic structure calculations reveal that the Cu introduces its d- and s-states within the gap and their energies and occupation depend strongly on the charge state of the defect. Experimental optical absorption spectra are well reproduced by the sole Cu1+ defect spectra, leading to the conclusion that in the as-grown material just Cu1+ centers are formed, with possible presence of small concentration of the Cu2+ centers. In the case of irradiated material, present study predicts formation of the interstitial Cu0 defects, whose presence should significantly change the optical absorption and emission of the material.