In this paper, given an integer e and n such that e|n, and a prime p, we propose a method of constructing optimal p2-ary low correlation zone (LCZ) sequence set with parameters (pn-1, pe-1, (pn -1)/(pe -1), 1) from a p-ary sequence of the same length with ideal autocorrelation. The resulting p2-ary LCZ sequence set can be viewed as the generalization of the optimal quaternary LCZ sequence set by Kim, Jang, No, and Chung in respect of the alphabet size. This generalization becomes possible due to a completely new proof comprising any prime p. Under this proof, the quaternary case can be considered as a specific example for p = 2.