This paper proposes a lifted domain ILC design technique for repetitive processes with significant non-repetitive disturbances. The learning law is based on the minimization of the expected value of a cost function (i.e., error norm) at each iteration. The derived learning law is iteration-varying and depends on the ratio of the covariance of non-repetitive component of the error to the covariance of the residual total error. This implies that in earlier iterations the learning is rapid (large learning gains) and as iterations go by, the algorithm is conservative and learns slowly. The proposed algorithm is also extended to the case where the learning filter is fixed and the optimal (iteration-varying) learning rate needs to be determined. Finally, the performance of the proposed method is evaluated vis-a-vis a geometrically decaying learning algorithm and an optimal fixed-rate learning algorithm through simulation of a Micro-robotic deposition system.