We present results of 13CO(1-0), C18O(1-O), and HCO+(1-0) map ob-servations and N2H+(1-O) single point observations directed towards a sample of nine low-luminosity 6.7-GHz masers. N2H+ line emission has been detected from six out of nine sources, C18 O line emission has been detected from eight out of ninesources, and HCO+ and 13 CO emission has been detected in all sources. In particular, a "blue profile" of the HCO+ spectrum, a signature of inflow, is found towards one source. From integrated intensity emission maps, we identified 17 cores in the sample. Among them, nine cores are closely associated with low-luminosity methanol masers. For these cores, we derive the column densities, core sizes, masses and molecular abundances. Comparison of our results with similar molecular line surveys towards the southern sky methanol masers indicates that linewidths of our sample, including only the low-luminosity masers, are smaller than the sample that includes both low-and high-luminosity masers. For the maser associated cores, their gas masses have the same order of magnitude as their virial masses, indicating that these cores are gravi-tationally bound systems. In addition, we have found from our observations that the low-luminosity methanol masers tend to coexist with H20 masers and outflows rather than with OH masers.