To add a little bit to Midnight's answer:
LEM is more of a listener, not a poller. If you want data to stop flowing into the LEM, you will typically need to control that from the node side.
For a syslog device that means changing the trap levels to control how much data, or disabling syslogging to stop the flow of data from the node.
As long as LEM is getting syslog data from the node and there's a connector configured, it will re-add the node.
You can delete the connector as well, but that won't stop your node from sending the LEM new data in the first place.