You can just send a closure to the UI thread and have it executed there, provided you are using a good enough programming language.
Or start the long-running computation from the UI code in a way that returns a promise, and chain the UI update on it, in a way that causes that continuation to be scheduled on the UI thread.
Or have an UI that can be updated from any thread (but not simultaneously) and take the big UI lock.
Or start the long-running computation from the UI code in a way that returns a promise, and chain the UI update on it, in a way that causes that continuation to be scheduled on the UI thread.
Or have an UI that can be updated from any thread (but not simultaneously) and take the big UI lock.