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LeBron James found a way to troll President Trump with his own catchphrase by rocking a hat with a similar sentiment ... and he did it while DJing live at a club.

LeBron grabbed dinner Saturday night with his wife, Savannah, at Komodo in Miami., after which he joined the restaurant's owner, David Grutman and Kim K pal Jonathan Cheban﻿, for some partying in their upstairs lounge.

We're told LeBron was put at the helm of the turntables and DJ'd for 2 hours straight -- all while sporting a red hat that said ... "Strive for Greatness" ... which looks an awful lot like Trump's "MAGA" hat.

Bron didn't address Trump during his DJ set, but the timing seems like anything but a coincidence considering the violent protests in Charlottesville the same day ...and his longtime stance as an anti-Trump guy. Plus ... there's this:

It's sad what's going on in Charlottesville. Is this the direction our country is heading? Make America Great Again huh?! He said that🤦🏾‍♂️ @KingJames