Can the state of Michigan, specifically the bureau of state lottery be
sued for patent infringement, or are they immune under a sovergn
immunity defensebased on the 1999 US Supreme Ct. case overruling the
1992 USPTO decision allowing state liability.
Secondly to answer the above question an assumtion or dertermination
of whether Michigan
Lottery considered to be engaged in a private function or who may or
may not be a privatized division or conducting a private function for
the state.

Governments are generally immune to criminal prosecutions but not civil penalties.

Based on the difficulty and expense of such a procedure I caution you
to consider  a cost-benefit analysis, i.e. how much do you stand to
win at best?

The simple way to decide is to see if you can find a lawyer who will
take this on a contingency basis.

I agree with your concern a cost-benefit analysis would need to be
done.  However, I am not sure there are many attorneys that would take
a case against the state under a contingency fee structure.  The mega
firms would touch it but a victory by attrition would shortly ensue. 
That is why I am looking to implement a Success Bonus structure as
used in Europe to entice a law firm to take a budgeted approach
towards litigation or licensing.