First, a little discussion what these methods do, the answer to your question is below that.
From the documentation of setNeedsLayout():
This method makes a note of the request and returns immediately. Because this method does not force an immediate update, but instead waits for the next update cycle, you can use it to invalidate the layout of multiple views before any of those views are updated.
Usually, you need to call this if there's some external factor affecting the layout that UIKit doesn't know about (e.g. old fashioned manual layouting code by overriding layoutSubviews()). It doesn't trigger an immediate re-layout, that usually only happens on the next main runloop iteration. This allows you to mark several views as needing layouts, you can call it on the same view multiple times within the same runloop iteration, but UIKit only does the actual layouting once (as I just noted, usually on the next runloop iteration).
But if you need the layout to get settled right now (e.g. because you need to measure its result), you need to call layoutIfNeeded().
If no layout updates are pending, this method exits without modifying the layout or calling any layout-related callbacks.
This is a crucial point about layoutIfNeeded(): if the layout system doesn't know there are pending changes, it simply won't do any. Calling setNeedsLayout() is the way we tell the layout system that there are changes that require a layout run.
If you only use auto-layout and manipulate just the constraints of the view you are about to re-layout, you can skip setNeedsLayout() since that has already been called indirectly; but setNeedsLayout() is very cheap, so there's no harm in calling it if you're unsure.
So, after calling setNeedsLayout(), do you need to call layoutIfNeeded()? To simply update the view on screen, no, you do not need to call layoutIfNeeded() since UIKit will do so on its own on the next main runloop iteration. In fact, you might negatively impact render performance if you always call layoutIfNeeded() even though your code doesn't need the updated layout right away since this can result in multiple layouting runs within the same runloop iteration.
But if you rely on the layout information immediately (for example, you need to measure the height of a view), you do need to call it. Just beware to have your design not do this too often.
Your comparison with "async" and "sync" is indeed somewhat fitting: in a way, you can see setNeedsLayout() as triggering an asynchronous operation and layoutIfNeeded() "waits" until it has happened (that's not what's actually going on, but from a certain point of view that is the observable effect).
