The Poland international's goals either side of an Ansu Fati finish helped the Blaugrana cruise to a comfortable victory at Estadio Manuel Martínez Valero.
Ferran Torres added a fourth as Xavi's side moved 15 points clear of second-placed Real Madrid in the table to further underline its domestic dominance this season.
For Sebastian Beccacece, Elche's fourth different boss of the season, it was a chastening reminder of the task at hand.
Barca pressed hard for an opener from the start and was duly rewarded 20 minutes in when Lewandowski turned in a Ronald Araujo header from Jordi Alba's free-kick.
But Lewandowski missed a golden opportunity to double the visitor's lead before the break with a flying header, as did Jules Kounde only for Edgar Badia to save his effort.
The Blaugrana were more ruthless in the second half, though.
Fati capped off a fluent breakaway move with a cool, low finish to put Barca two up in the 56th minute
Lewandowski was then on hand 10 minutes later, latching onto a Gavi throughball and dispatching a neat finish, before Torres brought down the forward's looping pass outside the box for a fine strike of his own.
That added a last touch of gloss to a dominant performance that edges Barca closer to silverware.