What are some common lessons learned regarding issues or pitfalls experienced when migrating a Department of Defense or other government accounting system to the cloud environment? Any wins or best practices to share?

i am not the government sector but i believer the financial section is a same thought.
Still the migrating to cloud is not matured enough to run the production services of any organization due to the critical services and risk measurement. But you can run on the cloud the test or development environment to facilitate the offshore resources to avoid any security dependances and speed up the product live cycle.    

These are some general best practices for cloud migration.

Select appropriate cloud provider.
Always have a backup. On-Premise is better.
Incorporate security and governance.
Make sure the app is cloud ready.