The Formula One race car driver was out Sunday on a beach in Barbados, where he was rockin' Bieber's Purpose Tour shorts ... the same ones the Biebs was seen in himself last week.

From the looks of these pics ... Lewis must've thought they were gym shorts, 'cause he's in full beach action mode ... catching footballs and hitting the water.

One thing's for sure -- he's got Bieber's look down lock, stock and barrel ... from showing off his tatted torso to even sagging a bit and giving Supreme some free press. Bieber did the same with Calvin Klein ... but he's got an endorsement deal with 'em.

So the question here is ... who did it better?