  The Molecular Ridge in the LMC extends several kiloparsecs south from 30
Doradus, and it contains ~30% of the molecular gas in the entire galaxy.
However, the southern end of the Molecular Ridge is quiescent - it contains
almost no massive star formation, which is a dramatic decrease from the very
active massive star-forming regions 30 Doradus, N159, and N160. We present new
ALMA and APEX observations of the Molecular Ridge at a resolution as high as
~16'' (~3.9 pc) with molecular lines 12CO(1-0), 13CO(1-0), 12CO(2-1),
13CO(2-1), and CS(2-1). We analyze these emission lines with our new multi-line
non-LTE fitting tool to produce maps of T_kin, n_H2, and N_CO across the region
based on models from RADEX. Using simulated data for a range of parameter space
for each of these variables, we evaluate how well our fitting method can
recover these physical parameters for the given set of molecular lines. We then
compare the results of this fitting with LTE and X_CO methods of obtaining mass
estimates and how line ratios correspond with physical conditions. We find that
this fitting tool allows us to more directly probe the physical conditions of
the gas and estimate values of T_kin, n_H2, and N_CO that are less subject to
the effects of optical depth and line-of-sight projection than previous
methods. The fitted n_H2 values show a strong correlation with the presence of
YSOs, and with the total and average mass of the associated YSOs. Typical star
formation diagnostics, such as mean density, dense gas fraction, and virial
parameter do not show a strong correlation with YSO properties.
