do trend and aging reports only work in the data warehouse?

The LQE data source added support for a limited number of trend reports in 603 -- primarily trends on total number of artifacts.

First, you have to enable the metrics collection jobs in the LQE Administration UI, as described in this Knowledge Centre topic:
https://jazz.net/help-dev/clm/index.jsp?re=1&topic=/com.ibm.team.jp.lqe2.doc/topics/t_configure_lqe_data_collection_ui.html&scope=null
Otherwise you won't see any data or options when you go to choose the trends for reporting.

Creating the report in Report Builder works the same as building trend reports with the DW; there are just fewer options to choose from. If there are specific trend reports you'd want to see supported using the LQE data source, please submit an RFE.

 A data warehouse is where such historical information for reporting is collected. I don’t see how this would ever change.

 LQE has metrics jobs - if it doesn't allow for trend data, then I'm a little confused too about why the metrics are available.