We report on novel variants of the flavin-based fluorescent protein iLOV with absorption and emission optical bands shifted to the longer wavelengths relative to their precursor. First attempts (J. Phys. Chem. B 2015, 119, 5176; 2016, 120, 3344) to improve spectral properties of iLOV, a fluorescent marker in living cells, showed that single point mutation Q489K could lead to a promising variant, but its realization was not successful due to unfavorable conformation of the flexible lysine side chain pointing away from the chromophore. The results of molecular simulations presented in this work evidence that location of the charged lysine residue near the chromophore isoalloxazine ring can be fixed by introducing additional mutations in iLOV. Several suggested protein variants are characterized by using classical and QM/MM molecular dynamics simulations followed by optimization of structures in the ground and excited states. Transition energies between the S-0 and S-1 states are computed by using the advanced quantum chemical methods TD-DFT, SOS-CIS(D), and XMCQDPT2. According to our simulations, the chromophore-containing pockets for the red-shifted iLOV variants containing lysine either at position 392 (V392K/F41OV/A426S) or at position 489 (Q489K/L470T) should be stable and exhibit absorption and emission bands red shifted by 40-50 run relative to iLOV.