VFR
The rules are pretty strict on how an un-certified aircraft can be operated by civilians. The ex-military Gazelles and Hueys that we see are all civil certified against a civil type certificate, the Lynx has no such coverage (at least I can find no reference to a civil version).
When a military aircraft is "civilized" it is sometimes modified to exactly fit its certified cousin, usually with some placards and small pieces of equipment that allows it to meet FAR. The FAA then deems it to be airworthy and issues a certificate for it.
Except for some limited warbird restricted category certificates, the purely military aircraft, such as Lynx, cannot be operated by civilians unless they are fully certified. Most military designs do not meet civil standards for handling, fatigue strength and safety of systems (a surprizing statement when most of the flying world sees military aircraft as somehow more rugged). Certification therefore means expensive redesign, and full qualification testing, a multi-million dollar investment.
One exception (that draws lots of flack on pprune) is when an aircraft is operated in the US by a public agency, which is generally exempt from FAR certification rules. A US State (like the US Federal Government) can actually "certify" an aircraft for its own use, so some ex-military aircraft are allowed into service as-is.
Here is a bit of background:
http://www2.faa.gov/certification/aircraft/awcertqa.htm