I would not even think about beak-notching, as Noodles mentioned that is a very old practice that was mistakenly thought to help, but not only does it not help at all, it often disables the bird's ability to eat, climb-up things, preen themselves, etc. So that's a no-go...
***I absolutely would have full, routine Blood-Work done ASAP, BEFORE you do anything as far as his lower beak goes!!! You can't do anything to help that particular issue without knowing what it's cause is, otherwise you'll just be pissing in the wind, so to speak, meaning you'll just be trying all kinds of different things, guessing what the problem is, and seeing what sticks, and that's not a good way of treating physical medical issues that are chronic, like beak issues. Most-all problems with their beaks as far as them growing abnormally/in the wrong direction, growing too fast, growing too slow, their beaks being too soft, being too brittle, etc. do have to do with a Deficiency in their levels of SOMETHING, but not necessarily Calcium, it could be a deficiency in any one of a hundred different Vitamins, Minerals, etc., or rather, most-commonly a combination of 2 or more! And with something like Castling or Scissoring of the beak, it's a continual issue that typically does not stop until the Deficiency is addressed...And the only way to start correcting the issue is to have full, routine Blood-Work done along with all of the Nutritional/Metabolic Panels so that you can get the WHOLE PICTURE of his Nutritional Health, find out what he is Deficient in AS WELL AS what levels are too high, which can cause just as many problems, then you consolidate the Blood-Work results by making a list of what he is deficient in, what he has higher than normal levels of, AS WELL AS ANY ABNORMALITIES IN HIS ROUTINE BLOOD-WORK, LIKE IN THE CBC (that's why you need to not only test his Nutritional Levels but also have a CBC, Liver and Kidney Panel, and the rest of the regular, routine Blood-Work done at the same time, because you absolutely need to know what else is not normal).
Once you get all of his Blood-Work back and you can look at the results and say "Okay, he's deficient in these things, he's got excess of these things, and these results in his CBC, Liver/Kidney Panesl, Chem 7 Panel, etc. are abnormal."...Only then can you (and your Avian Vet) come-up with a full "Differential-Diagnoses" list and really get to work on actually diagnosing what the underlying-condition or conditions that are causing his health issues are, and then making appropriate treatment-plans. Otherwise you're just wasting time and money on doing "Treatment Trials" over and over and over again until you find something that sticks, and usually this method doesn't end with any Diagnoses nor finding any treatments that are successful...
***The other reason you need to get full, routine Blood-Work along with his Nutritiona-Levels done is because it's very possible that whatever originally started causing his Plucking is related-to whatever is causing the Castling of his lower-beak, or possibly even THE SAME, UNDERLYING CONDITION(S)!!!
***The Beak, Toenails, Feathers, and Skin are all very closely-related to one another, Specifically from a Nutritional/Constituent point of view; they all require the same individual Vitamins, Minerals, Enzymes/Amino Acids/Proteins, and other Nutritional sources like fat, sugars, fibers, etc. to start growing and to continue to grow...So the likelihood of whatever originally caused Lincoln to start Plucking himself and whatever is causing the Castling of his Beak being related or even the same is extremely high. And it's very normal for a bird to start plucking themselves due to whatever underlying physical/medical issue and to continue to pluck themselves for years and years if the underlying-condition isn't found and corrected, and THEN years later the same underlying issue finally also starts to effect other parts of the bird's body, like the Beak, the Toenails, the Skin, the inside of their Mouths/Mucous Membranes, etc. because the underlying problem/condition has always and still does exist and was never diagnosed nor treated...And the reason this is so common is because very quickly the act of plucking does in-fact become an addiction to the bird, and we, their owners and their Avian Vets, tend to forget about finding the underlying cause of the plucking in the first place because we know that now it's a pschological/behavioral addiction. And while this is true, if the underlying, original cause is never diagnosed or treated, the possibility of it causing a score of other health/medical issues in the future is extremely high and extremely probably, and the problem with this is that these additional health/medical issues are usually treated like totally separate problems. In fact, in most cases the bird being a long-time plucker is never once even mentioned throughout the diagnosis and treatment of the new conditions!!! And this vicious-circle usually just contiinues throughout the remainder of the bird's life, which may or may not be shortened because they've suffered for so long with a disease, deficiency, etc.
I think having the cultures/swabs done and ruling-out any type of Bacterial or Fungal Infections, Parasites, etc. was absolutely step #1 in trying to figure out what is going on and trying to treat it. But usually there is no step #2 in this process for one reason or another...But the fact that Lincoln is also suffering from Castling/Scissoring of his Beak is a huge reason to move onto step #2, which is full, routine Blood-Work with Nutritional-Level testing. And you never know, once you get his Blood-Work back and you start treating the causes of his Beak Castling, that treatment may also noticeably improve his plucking!!!
***As far as giving Lincoln Probiotics, I have no idea why your Vet would tell you to only give them to him once a week. I've not ever heard of a Vet suggesting that, nor have I ever heard of anyone following that instruction, so I really can't comment on it...I have always given all of my birds and my Bearded Dragon a daily Probiotic supplement (both Birds and certain Reptiles, specifically Beardies, are extremely prone to Fungal/Yeast Infections and to having their level of beneficial-Bacteria drop-off), just like I myself and many other people take a daily Probiotic supplement...Now of course you need to choose a Probiotic supplement that is specifically meant for birds/parrots, such as the Qwiko Avian Probiotic powder or the BeneBac gel/paste or their powder, because the dosing is specifically measured for birds; but I've not ever read any dosing-suggestions on any Probiotic supplement that didn't also say that it's a daily supplement. The only things I can say from the opposite point-of-view from your Vet's are #1) Based on how Prebiotics and Probiotics work, I can't imagine that giving ANYONE (person, bird, dog, reptile, etc.) one dose of them per week, or even twice a week is going to do a whole lot of good, because they are meant to build-up throughout the GI Tract over-time, with the idea being that eventually the normal, healthy Flora being added by the Probiotics will reach the optimal-population for the specific animal/bird, and then that the continual daily-dose of Probiotics will result in a constant, optimal environment to the benefit of the animal/bird etc...and then #2) Quite simply, if you're using a Probiotic formulated specifically for birds/parrots and you're giving them the correct, pre-measured dose of the powder, gel, paste, etc., there's no down-side to it...Even if the Probiotics don't help anything or do any good, for example if there is a serious health issue in the Gut that is causing the constant growth of Fungi, or is causing the pH of the Crop, Stomach, Intestines, etc. to be constantly to high or too low, rendering the Probiotic Bacterial-Strains inactive, there STILL IS NO HARM that the Probiotics can cause, even if say you were to happen to accidentally give an extremely high dose one day, the worst that could happen would be a bit of diarrhea later that day...
I just think that if you don't give your bird, yourself, your dog, etc. the Probiotics dose once-daily, especially since each specific formulation of Probiotics has a directed-dose that is measured-out to be given once-daily (or whatever the dosing directions for each specific brand are; I've not ever seen one that wasn't "give the pre-measured dose once-daily"), then it's not going to do any good because it won't ever get the chance to build-up in their Gut, reach the optimal flora-population, and then maintain the optimal, healthy environmental-stasis throughout the entire GI Tract, which is the entire goal of taking a Probiotic to begin with...
