How Do I Find the Best Lumineers Dentist?

Lumineers, like any cosmetic dental work, require great skill, experience and diagnostic ability on the dentist's part. And Lumineers require special training before the dentist is allowed to place them. Lumineers are just a specific type of porcelain veneer. The actual product that the dentist uses is less important than the training, skill and expertise he/she has.
You should ask the dentist how long he/she has been performing this kind of procedure, what advanced training he/she has, how many patients he/she has treated, how complex were the cases that were treated, what other options you may have available, etc. Most dentists are happy to show you before and after pictures of their work, especially patients they have treated who presented with similar situations to yours.

Use the same guidelines you would in trying to find the best cosmetic dentist.
Look for credentials, lots of continuing education, visit a few offices, look for photos and before/after photos of the dentist's OWN work.
Remember that the dentist may place a different brand name of veneers (other than Lumineers brand) -- they may use an even better brand.

I think you should not narrow your range to best Lumineers dentist.  I would find a cosmetic dentist.  Lumineers are jsut prepless veneers made with a specific brand of porcelain.  It is an elaborate direct to public marketing program that charges dentists to be a "Lumineer Dentist" to get referrals.  You should seek out a dentist that does cosmetic work that you are impressed with and then review before and afters with him or her and why your teeth should be prepped or not prepped in a particular way.  Lumineers (which are just a branded form of porcelain for direct to public marketing) may not be the best option for you.  FInd the results you like.  Interview a lot of cosmetic dentists and then you will be able to make an educated decision.

"Best" is pretty subjective, so only you can answer that question. A reliable method to choose is to simply have some consultations with dentists that have been recommended and some that you find from your own efforts.
Lumineers is a brand of porcelain, and has been around a long time. The key to a fantastic result is the care, skill and judgment of the treating dentist, as well as the advanced training the dentist has achieved. Ask for photos of similar cases to yours to show what each dentist has actually done (some purchase books of stock photos).
You may find that Lumineers is not recommended for your case, in which case an alternative material would be suggested.