I wouldn't overdo it, but certainly you can start a light study schedule now. However, I would consider taking a real test in early 2022 to see how you do. If you are lucky, you might reach your target score and not need to retake the test.
If your professor gave you a good grade in your class, you can just remind them of who you are and the quality of your work, and I'm sure most would be happy to give you a letter of recommendation.
To be frank, I wouldn't bother to retake to gain 2 points. Your 168 already probably makes you competitive for most of the top law schools. What's your UGPA? But good luck since you have already registered for November. If you don't improve, submit …
A 144 is really going to limit your options, however. I would attempt to get a 150 on the next test. If you don't, just apply to the schools where you have a realistic chance with a score in the 140s and follow the plan above.
I probably wouldn't bother with a 165 and your GPA. If you score a few points above or below a 165 on the 4th test, that will make little difference. You can get into a T10 with those numbers. I'd start applying now and forget the 4th test.
I'm one and done for this test, assuming I don't get below a 155. Otherwise, I will proceed with my applications as I'm not seriously trying for a Top 50 school.
I would take the October LSAT, hope for the best, and then apply to all the schools you are willing to go to after you get your score. You certainly aren't guaranteed a spot at Harvard even if you get a 173 or even a 175.