The agency said it is investigating San José State University, the University of Pennsylvania and a middle and high school athletics association.
The lawmakers want details, including who in the Elon Musk-led agency has access to sensitive data and the steps taken to protect that information.
The lawsuit alleges that President Donald Trump's orders overstep his authority, use overly vague language and intend to chill speech he opposes.
Since congressional approval is needed to shut down the agency, experts say the more likely scenario is a combination of budget cuts and restructuring.