the LRPC is becase in the long run, unemployment tends to stay where it's NAIRU/natural rate of unemlpyment is. ie if your natural rate of une is 5.5%, in the short term, it could go above or below this rate and thus the short run phillips curve occurs (where une can reach above NAIRU and inflation will decrease)
However in the long run, unemployment tends to settle at the NAIRU...so it never really exceeds 5.5% in the long run....therefore there is a limit as to how much une can fall and inflation to increase with it. which is why the phillips curve and the trade off is only short term