Accelerated life-testing (ALT) is a very useful technique for examining the reliability of highly reliable products. It allows testing the products at higher than usual stress conditions to induce failures more quickly and economically than under typical conditions. A special case of ALT are step-stress tests that allow experimenter to increase the stress levels at fixed times. This paper deals with the multiple step step-stress model under the cumulative exposure model with lognormally distributed lifetimes in the presence of Type-II and Progressive Type-II censoring. For this model, the maximum likelihood estimates (MLE) of its parameters, as well as the corresponding observed Fisher Information Matrix (FI), are derived. The likelihood equations do not lead to closed-form expressions for the MLE, and they need to be solved by means of an iterative procedure, such as the Newton-Raphson method. We then evaluate the bias and mean square error of the estimates and provide asymptotic and bootstrap confidence intervals. Finally, in order to asses the performance of the confidence intervals, a Monte Carlo simulation study is conducted.