In recent works we proposed a lazy algorithm for reachability analysis in networks of automata. This algorithm is optimistic and tries to take into account as few automata as possible to perform its task. In this paper we extend the approach to the more general settings of reachability analysis in unbounded Petri nets and reachability analysis in bounded Petri nets with inhibitor arcs. We consider we are given a reachability algorithm and we organize queries to it on bigger and bigger nets in a lazy manner, trying thus to consider as few places and transitions as possible to make a decision. Our approach has been implemented in the Romeo model checker and tested on benchmarks from the model checking contest.