It's funny, but I didn't notice the slight sync issues at the theatre, but I do see it on the Blu-ray, albeit only slightly during some musical numbers that always had rubbery sync anyway.
I couldn't find MY FAIR LADY at any store locally in Columbus. I ended up ordering it from Amazon.com.
Here is a 1080p comparison of both Blu-ray releases:
https://www.dropbox.com/s/dr0migsub6cgj5m/myfairladycomparison.mp4?dl=0