Compute Lazily - Model checking
In computer science, "lazy" means "just in time": in other words, you defer doing a computation until the last possible moment (e.g., until when the output is needed).

In computer science, "online" means that you are processing a bunch of input in a streaming fashion.  For instance, you might be given a sequence of queries.  An online algorithm would immediately answer each query.  In contrast, an offline algorithm might wait until it has seen all the queries before answering any of them.