Your agency should be the innovation lab. The problem with cordoning off an area as the official place for innovation is that it may be ignored by the rest of the organization. Think of the XEROX PARC example in which that innovation lab essentially built the modern GUI computer but their innovations were ignored by XEROX.
Instead of "space" think "time." Many innovative companies give their employees 10% to 20% of their work time to devote to personal projects that they later pitch to the organization. http://www.computerworld.com/s/article/332900/Innovation_and_the_20_Solution
When you make every employee an innovator, then you truly have your innovation lab.