I am trying to find out if the US Department of Veteran Affairs Austin Outpatient Clinic is leased by the government or owned outright. Where do I find this information?
You can search the Government Services Administration's Inventory of Owned and Leased Properties to find out what buildings the government owns or leases. The VA's Austin Outpatient Clinic is located at 7901 Metropolis Drive, so I searched the inventory for government leases in Austin, TX:
You can search the inventory by city, city/state, and Congressional district, among others.
Most cities these days put their property records online. Austin's are available at http://www.austintexas.gov/GIS/PropertyProfile/. You can search Google Maps or the website of the organization in question to find the address, and then search the city property records system for that address. If the address is owned by someone else besides the organization in question, then it's safe to say that they are renting or leasing.
Note that property investors frequently make LLCs just to be the legal owner of a particular property, but large organizations generally don't.