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LKY was a Hakka baba lar..Peranakans speak Malay because their father is from China but their mother is a Malay. Children tend to learn to speak whatever their mother speaks and after a few generations, Malay or rather a form of Baba Malay is spoken by baba and nonya.

LKY speaking Malay is like your Pritam Singh speaking Punjabi as his mother tongue.

LKY's mother is not Malay, but do have Peranakans heritage 
https://en.wikipedia.org/wiki/Chua_Jim_Neo

Years ago I was told by my Malay friend,
that the Malay language that LKY spoke is the Official Malay language like Mandarin use as official language
There are number Malay dialects, 
https://www.youtube.com/watch?v=XOrzzqEubNs

Almost every countries have dialects that include Japan. 
https://www.youtube.com/watch?v=eVwZosGJ6wA

Normally the Capital use language will be the official language.