[whpalmer4]

I think that the lead time pushes it out by however much time in overall project availability units. Note that this is not necessarily the same as the availability of the resource. If I set up a half-day-long action for Thursday, and a milestone with a 3 day lead time connected to it with a Finish->Start dependency, with the default settings, that milestone shows up mid-day Tuesday, which is 3 days on the project work schedule later. Even if all my resources are listed as unavailable, that's when the milestone will appear, because it isn't dependent on a resource. If I set the normal work week for the project to be 7 days a week in the resource calendar editor, the milestone will end up mid-day Sunday, which again is 3 days on the project work schedule later -- even if all of the resources are listed as working only M-F!

Another way of delaying something is to make a task to occupy the delay, and assign it to a material resource called Delay or Time (be sure to allocate plenty of units if you might have overlapping delays). Again, you'll need to exercise some care with the availability/scheduling of that resource's work week if you want the clock to run while everyone is loafing at home on the weekends.

If that didn't answer your question, maybe you could upload an example of what you're trying to do?