Transitions from the A (1)Sigma (+)(u) (v = 4, J = 11 and 9) level to the F (1)Sigma (+)(g) (v = 3, J = 10) and 2 (1)Sigma (+)(u) (v = 2, J = 10) levels of the (LiLi)-Li-6-Li-7 molecule, were observed using Doppler-free two-step polarization labeling spectroscopy. The intensity ratio of the two transitions was approximately 150:1. The energy spacing between the deperturbed F (1)Sigma (+)(g) (v = 3, J = 10) and 2 (1)Sigma (+)(u) (v = 2, J = 10) levels was calculated to be 0.11 cm(-1). The 2 (1)Sigma (+)(u)<--A (1)Sigma (+)(u) transition becomes allowed due to an interaction between gerade and ungerade states resulting from the mass difference of the nuclei. The interaction energy between the F (1)Sigma (+)(g) (v = 3, J = 10) and 2 (1)Sigma (+)(u) (v = 2, J = 10) levels was calculated to be 0.009 cm(-1) from an analysis of the deperturbed level energies and the ratio of the line intensities.