ORFEUS far UV echelle spectra have been used to investigate HI, Hz and CO absorption lines along the line of sight towards LH 10:3120 in the LMC, extending the study presented by de Beer et al. (1998). While Hz absorption is clearly visible, no CO absorption at LMC velocities is detected, but an upper limit of N(CO) less than or equal to 3.3 x 10(13) cm(-2) for the CO column density is derived for the C-X band near 1088 Angstrom. The detected Hz absorption features were used to determine a limit for the H-2/CO ratio of N(H-2)/N((CO)-C-12) greater than or equal to 2.0 X 10(5) for the LMC gas along this individual line of sight. Generally, the fraction of gas in molecular form in the LMC is low compared to interstellar gas in the Milky Way with the same total gas quantity. We compare the absorption spectroscopy with SEST CO emission line measurements. It is found that most of the CO emission comes from gas behind LH 10:3120. We discuss our results in view of the possible scenario, in which the low dust content limits the amount of molecular hydrogen in the diffuse LMC gas.