The LRPC defines a (theoretical) inverse relationship between inflation and unemploymemt.. i.e. it simply looks at the relationship between the two variables. It doesn't define what should be a 'natural' rate of unemployment.
The NAIRU attempts to define what governments should perceive as a 'natural' rate of unemployment. i.e. if unemployment is at, or below, a certain level (=the NAIRU) then governments should not feel constrained to act (by economic reasons) to reduce unemployment. The NAIRU is defined by reference to the LRPC (i.e. data on the LRPC is taken as defining the edge of the 'normal' range) but it is not the same as it.
Two references from Wikipedia:
http://en.wikipedia.org/wiki/Phillips_curve
http://en.wikipedia.org/wiki/Phillips_curve
Hoping this helps,
Chris