You should see entries like this:
LAS 2014-12-10T07:48:09.417 -0600 INFO - ProductServerAction - START:
http://gazelle.weathertopconsulting.com:8282/baker/ProductServer.do?xml=<lasRequest href="" match="/lasdata/datasets/coads_climatology_cdf/variables/airt"/><region><range type="x" low="21" high="379"/><range type="y" low="-89" high="89"/><point type="t" v="15-Jan"/></region></args><link match="/lasdata/operations/operation[@ID='Plot_2D_XY_zoom']"/><properties><ferret><view>xy</view><size>.8333</size><image_format>gif</image_format><annotations>file</annotations></ferret><las><output_type>xml</output_type></las><product_server><ui_timeout>10</ui_timeout></product_server></properties></lasRequest>
In your $TOMCAT_HOME/content/las/logs/log* files.
Each one of those is a request for an LAS product and the first "<link match=" is the LAS id of the parameter being requested. You can also differentiate as to what the user did by the "link match=" that contains the "operations/operation" by the ID.
We don't have any facilities for analyzing the logs, but maybe some of these public domain or commercial log analysis programs can be made to work. Or some fancy grep and sed could make some basic statistics. You can't identify the user, but there might be a way to match up the requests based on other logging information you collect.
Roland