A customer run into this issue: “It takes approximately 90 seconds or longer to license Revit 2013/2014, even though our Flex licensing server is on the LAN. It only takes 20 seconds to license AutoCAD, but 7x longer for Revit.”
I was not able to find the solution but eventually the customer found out that “we discovered that we were running an antiquated version of the FlexLM server. When we set up our new server, we used the latest version. This solved the Revit licensing delays. It just takes 10 seconds for all versions of Revit to license.”
So in case you also run into this kind of slow startup of Revit or possibly other programs try to upgrade the FlexNet license manager/Autodesk network license manager.