Go look up this, go look up that. Go look up Stern-Gerlach, go look up the double slit experiment, go look up Lorentz transformations, go look up Feynman, go look up aberration. I know the routine. It does not instill the impression that you know what you are talking about.
why should I answer your question?
Indeed this is a very good question. You were able to informally estimate that the apparent position of Sirius is very close to its actual position. And you were able to easily assert that the apparent position of the Sun lags behind its actual position by 8.3 minutes or 2.1 degrees. It should be no trouble at all for you to whip out your calculator, merrily grind away, and give an estimate of the lag between the moon's apparent position and its actual position. There's no thought-experiment to mull over. It's merely a question about the moon. If your idea about solar lag is correct, there should be nothing alarming about this lunar lag question. It shouldn't trouble you at all.
Unless, of course, you have noticed some inconsistencies in your notions of physics and astronomy. Or doubts have set in, perhaps as a result of what has been said in other posts. If so, it is understandable that you have very much to fear from a simple and obvious question concerning the moon, and that you would at all costs avoid answering it, rather than face the collapse of the LeGrandeic System of musical spheres.
The lag is a little over a second. Do you feel better now?
Now can you answer my question?