The origin and long-range correlation of the director tilt in the recently discovered Lα'* phase, which is the lyotropic analog of the thermotropic smectic C* (SmC*) liquid crystalline phase, are investigated. Polarized micro-Raman spectroscopy reveals that the director tilt in the Lα'* phase originates from a tilting of the aromatic 2-phenylpyrimidine cores of the surfactant molecules. Optical measurements of the tilt angle show that its magnitude decreases with increasing solvent concentration, suggesting that the long-range inter-lamellar correlation of the tilt directions is reduced at increasing thickness of the solvent layers. The phase diagrams with four different solvents (water, formamide, N-methylformamide, N,N-dimethylformamide) are investigated, showing that the Lα'* phase is only formed with those solvents that exhibit a dense network of hydrogen bonds. This observation suggests that these hydrogen bond networks play an essential role in the long-range correlation of the director tilt between adjacent surfactant layers. To verify this assumption, mixtures with deuterated solvents are investigated, showing that the tilt angle in the Lα'* phase is indeed reduced by this modification of the solvent's hydrogen bond network.