A theoretical spectroscopic study is performed for the C state of LiH using eight diabatic or adiabatic states of symmetry (1)Sigma beyond the Born-Oppenheimer approximation. For the position of the vibrational levels, an excellent agreement is found with the ten recently observed ones giving confidence to the present study. The vibrational levels present rather strong vibronic shifts (rising to about 10 cm(-1) for upsilon = 37) particularly for the highest ones. Two approximate methods are tested for their estimation and a new method is presented for the evaluation of the vibronic part of the adiabatic correction. The new method involves the diabatic picture and the discrete variable representation. It leads to nonlocal corrections but avoids the calculation of radial couplings. Nonradiative lifetimes are accurately determined. They range over six orders of magnitude, from nanoseconds to milliseconds. Similarities of the LiH molecule in the C state and in higher excited states at large internuclear distances with highly excited Rydberg atoms are emphasized.