Context : Aims : N113 is an HII region located in the central part of the Large Magellanic Cloud ( LMC ) with an associated molecular cloud very rich in molecular species . Most of the previously observed molecular lines cover the frequency range 85–270 GHz . Thus , a survey and study of lines at the 345 GHz window is required in order to have a more complete understanding of the chemistry and excitation conditions of the region . Methods : We mapped a region of 2 \aas@@fstack { \prime } 5 \times 2 \aas@@fstack { \prime } 5 centered at N113 using the Atacama Submillimeter Telescope Experiment in the ^ { 13 } CO J=3–2 line with an angular and spectral resolution of 22 ^ { \prime \prime } and 0.11 km s ^ { -1 } , respectively . In addition , we observed 16 molecular lines as single pointings towards its center . Results : For the molecular cloud associated with N113 , from the ^ { 13 } CO J=3–2 map we estimate LTE and virial masses of about 1 \times 10 ^ { 4 } and 4.5 \times 10 ^ { 4 } M _ { \odot } , respectively . Additionally , from the dust continuum emission at 500 \mu m we obtain a mass of gas of 7 \times 10 ^ { 3 } M _ { \odot } . Towards the cloud center we detected emission from : ^ { 12 } CO , ^ { 13 } CO , C ^ { 18 } O ( 3–2 ) , HCN , HNC , HCO ^ { + } , C _ { 2 } H ( 4–3 ) , and CS ( 7–6 ) ; being the first reported detection of HCN , HNC , and C _ { 2 } H ( 4–3 ) lines from this region . The CS ( 7–6 ) which was previously tentatively detected is confirmed in this study . By analyzing the HCN , HNC , and C _ { 2 } H , we suggest that their emission may arise from a photodissociation region ( PDR ) . Moreover , we suggest that the chemistry involving the C _ { 2 } H in N113 can be similar to that in Galactic PDRs . Using the HCN J=4–3 , J=3–2 , and J=1–0 lines in a RADEX analysis we conclude that we are observing very high density gas , between some 10 ^ { 5 } and 10 ^ { 7 } cm ^ { -3 } . Conclusions :