I think there are two issues here. Firstly, this should be posted to an
ocological/conservationist/etc. newsgroup, not a gardening one. Secondly, Lynx
are unlikely to catch/eat deer if there are easier things to catch such as the
domestic cat, sheep, etc.

Reintroducing lynx isn't practical, and may well turn out to be a disaster, if
it was ever seriously attempted. There are better options to achieve the
results you seem to be looking for.

Dave.