Are there any methods to remove ALL scalp hair in lichen planopilaris to stop the progression and get a uniform look?

This difficult to answer without pictures and needs an in-person evaluation. Diode, alexandrite and yag lasers work best for hair removal. It will take a series of treatments and some people need treatments to maintain. See an expert in laser hair removal for best results. Best, Dr. Emer

Hair removal  on the scalp is long term but not permanent. You will need to do follow up sessions as you will probably have some areas of regrowth. This treatment  is also expensive as many sessions are necessary. As hair research is progressing rapidly, you may want to consider that in the future,  hair cloning and other methods of hair regrowth not available presently may be able to restore the areas. 

First you need to address the root the autoimmune system dysfunction you have. This is likely but one symptom of possibly many other symptoms that may manifest in the future should your autoimmune system decide to attack something else. Think arthritis or worse (God forbid).
I very much encourage you to seek out a good Integrative Medicine or Functional Medicine practitioner. They will likely identify the problem and help you resolve it at the root. Don't wait! The longer a problem exists it is generally harder to fix. Should it go too long, you'll need something like umbilical cord stem cell therapy to obtain a cure (expensive and only available outside the USA).  80 to 90% of autoimmune disorders start in the gut. Start off by going gluten free, but get to the type of doctor I described above. 
Assuming you get the problem addressed, you may wish to consider keeping the hair you have left and opt for a hair transplant. Should you still desire to be permanently bald, you can always have laser hair reduction performed.
I hope I have helped. Wishing you the very best.
Warmly,
Arbella Sarkis, MD    

There is not any way to PERMANENTLY remove ALL remaining hair from the scalp to stop or limit the inflamamtion . You would better to get  medical therapy of you may use razor cut all hair. .

IF you are a male and have LLP and are willing to shave your head, you can have the look of a full head of shaved hair, even without it, by getting Scalp Micropigmentation