I'll add a few things to help the cause. The ball loosening up in a few tows, points to a large problem.
From the posts, you are using a lock washer. This is good and for sure needed. If it is not a new one, consider getting a new one. The edge sharpness and strength is better on a new one. But also make sure the grade of steel of the lock washer is correct. If you do not know what grade to get, get a grade 8 lock washer.
Next is the tow ball. There is a "dry" threads torque spec for that ball as required by standards. And the torque spec changes pending the rating of the tow ball as the grade or temper of the steel changes with the rating. One torque number does not always fit all. Stamped on top of the ball is the pull rating which must be equal to or greater then the weight you are towing. Make sure the rating is correct.
There should be a manufacture on the ball top as well and then measure the thread shank size. Armed with that info, the manufactures web site will most likely have the correct torque based on "dry" threads. Or call them.
Using a lube on the threads requires the torque be adjusted down from the dry threads spec. Yes, using lube requires less torque to have the same bolt thread preload (tension). How much depends on the lube. Sometimes it may be a 15% to 25% reduction. If you use it dry, most are waxed from the manufacture and the spec they give covers this. If the tow ball is a low grade of steel, and you lube the threads and you did not adjust down the torque, you can by accident over torque the threads into the yield zone and that will allow the threads to stretch and come loose.
To create the correct amount of tightness, a torque wrench is the easiest. There is a torque to position method but this needs to be derived from a set of tests. For a towing application, I can't recommend using a large wrench with a 4 foot pipe as this may be way too much for a low strength ball (stretching the threads) or not enough for a high strength ball. (not enough preload (tension) to set the threads in the proper tension range for anti fatigue and loosening)
There is another thing not mentioned. Grease the tow ball when in use. You can use any type of wheel bearing grease if that's what you have or a white grease made for tow ball applications. This helps save the ball coupler on the trailer and scoring of the tow ball. If the tow ball and coupler are very dry, that high friction can aggravate loosening a tow ball. It does not happen all the time, but it does happen. Put a baggie on the greased ball when not in use. If not, that grease seems to have a magnetic attraction to ones pant legs.... At least mine anyway.
If you select the blue loctite, (removable) this may not fix the underlying issue. Something is not right, but what? Adding blue loctite on this fine thread step up may make the situation worse trying to ever get the nut off. It adds friction which is what it is supposed to do but after towing with it, that friction will be real high come the day several years from now trying to get it off. It may gall worse getting it off with removable loctite then just plain dry threads.
Also, is the hole in the draw bar or hitch head have a lot a play in it? Meaning someone put a 3/4" ball shank in a 1" hole? This is an issue, an adapter sleeve is suppose to be used in this case to take up the play.
Most times, a fastener loosening up like a tow ball comes from the fastener not being strong enough, (too light a tow ball for the load allowing thread stretch), lack of the proper clearance hole size, (missing an adapter sleeve create a sloppy fit), lock washer not correct for the application (maybe a weak one used) and the nut was not tighten correctly for the application. (too much or not enough torque)
Hope this helps
John