The two are completely independent of each other. We use both NPM and LEM. Our LEM install is a recent deployment and the two have not interfered with each other in any way.
Assuming that you know for sure that the node went down, I would check that the node is in NPM, and check its alert history on the node page. Check the logic of the alert to make sure there are no conditions that would suppress it from firing and maybe test it for that node.