In American English there is a clear difference, but do the words 'lawyerly' and 'loyally' actually sound the same in British English?
It will depend which British accent. They are homophones in my own south-eastern, non-rhotic accent.
They are not in the rhotic accent where I live (south-west). Which, I assume, is the reason they are not homophones in the USA.
I can't speak for other accents but the vowels may differ in other parts of the country, even if the accent is non-rhotic.