Does Indiana law prohibit any government lawyers from providing legal services outside of government employment?

Yes. For example, full-time prosecutors and full-time deputy prosecutors are required to devote their full professional time to the duties to the prosecuting attorney office. I.C. 33-39-6-6.
Even if no law prohibits pro bono service, you should always check with the leadership of your agency or office about practicing law outside of your government employment before commencing such work.