How big of an increase have you experienced?
LCP echo packets themselves are very small and should not impact consumption. The consumption would depend on the running services and hosts within RUTX's LAN. Additional monitoring would be required to detect the sources of consumption. For this, I would advice to install tcpdump package from Services -> Package manager, if it is not installed by default.
Otherwise, navigate to System -> Administration -> Troubleshoot page, under the Troubleshoot section, enable TCP dump, select interface wwan0. And leave it running for some time, then download the file.
Also, do you have remote HTTP(S) or SSH WAN enabled to access the device remotely, on their standard ports?