In this paper we present a linear computational complexity framework for design and implementation of (constrained) lifted Iterative Learning Control (ILC) systems with quadratic cost. The problem of designing constrained lifted ILC with quadratic cost is formulated as a convex optimization problem. We solve this problem using the primal-dual interior point method. High computational complexity of the primal-dual method, which render this method computationally infeasible for high dimensional lifted ILC systems, is significantly decreased by exploiting the sequentially semi-separable (SSS) structure of lifted system matrices. More precisely, O(N3) computational cost of one iteration of the primal-dual method is reduced to O(N), where N characterizes the size of the lifted system matrices. Furthermore, by exploiting the SSS structure the large lifted system matrices can be efficiently stored in computer memory. We also show that SSS structure can be exploited to efficiently implement analytical solution of the unconstrained lifted ILC problem with quadratic cost and for calculation of the norm and stability radius of ILC system.