While there have been some Alfred-as-Batman stories throughout the years (at one point Alfred "tried on" the Batsuit and got hit on the head so he thought he was Batman), I don't think that's an actual Batsuit. Instead, it looks like it's a subtle tribute to William Austin, the man who first portrayed Alfred in the 1943 Batman movie, and whose likeness redefined the role (the original Alfred was much fatter)
Austin's portrayal of him as a thin, proper English gentleman continues to be how people portray Alfred for the most part.
The Lego Batman Alfred costume has several similarities here, notably the old-style cap, the butler-as-valet topcoat, white gloves (the hands are white), and the pocketwatch (which has kinda been an Alfred Pennyworth staple, because what English gentleman didn't have one?)
The mask is in keeping with the mask that Robin of the same time period wore (minus the Batman curls)
The logo on the hat is also the original Batman logo