Forty-two vibrational (v = 2-43) levels of the (LiH)-Li-7 C (1)Sigma(+) excited electronic state have been observed by a pulsed optical-optical double resonance fluorescence depletion spectroscopic technique. The absolute vibrational numbering of the C(1)Sigma(+) state is identified with the measurements of the isotopic shifts between (LiH)-Li-7 and (LiH)-Li-6 among several rotation-vibration bands of the C(1)Sigma(+) -A(1)Sigma(+) electronic system, and it is further demonstrated by the consistency between observed spectral intensities and calculated ones. The highest observed quasi bound rotational level for the v = 43 level is J = 8. The spectral term values for those vibrational levels lying above v = 33 occur in an irregular order. The level of v = 34 lies mainly in the inner, tiny well. The term values for the observed rovibrational levels (2 less than or equal to v less than or equal to 32, 0 less than or equal to J less than or equal to 11) in the outer ionic well are described by a set of Dunham-type coefficients, with which a Rydberg-Klein-Rees (RKR) potential energy curve is constructed. This RKR potential is combined with an ab initio potential to construct an effective hybrid potential. The calculated electronic transition moment function for the C-A transition is also given.