Doppler-free UV-visible optical-optical double resonance polarization spectra of the 2 (1)Sigma(u)(+)<-- X (1)Sigma(g)(+) and C (1)Pi(u)<-- X (1)Sigma(g)(+) transitions in Li-7(2) molecules were measured. In the case of the double minimum 2 (1)Sigma(u)(+) state transitions to all vibrational levels (except the lowest two) localized in the inner potential well, to several levels in the outer well and some levels beyond the potential barrier were observed. Potential energy curves of the C (1)Pi(u)(v=0-10) state and the inner well of the 2 (1)Sigma(u)(+) state are determined by the RKR method. A V(R) curve describing the whole potential of the 2 (1)Sigma(u)(+) state (including both wells) is constructed using the Inverted Perturbation Approach (IPA). Tunneling splittings and energy shifts of the 2 (1)Sigma(u)(+) levels were observed, and their magnitudes are well represented in a semiclassical model using the IPA potential. Perturbations between the C (1)Pi(u)(v,J) and 2 (1)Sigma(u)(+)(v',J) levels were detected in the region above the potential barrier of the 2 (1)Sigma(u)(+) state, where the rotational constant of the 2 (1)Sigma(u)(+) state is much smaller than that of the C (1)Pi(u) state.