The letters L, M, N, O, P, Q, R, S, and T are substituted with integers from 1 to 9, but not in the order given. 4 is assigned to P. The difference between P and T is 5, so $T = P + 5$. Since P is 4, $T = 4 + 5 = 9$. The difference between N and T is 3, so $N = T - 3$. Since T is 9, $N = 9 - 3 = 6$.

Therefore, the integer assigned to N is 6.