With Juventus losing at Roma and Napoli held to a draw by Sampdoria, Lazio had the opportunity to make up ground on the top two, but they did not even make a contest of it against the struggling hosts in a one-sided game at the Stadio Artemio Franchi.
Innocent Emeghara was on target twice for Giuseppe Iachini's side, while Alessandro Rosina also beat Federico Marchetti in the Lazio goal.
The visitors rallied late on, but could not even find a consolation as they warmed up for their Europa League clash with Borussia Monchengladbach on Thursday night in far from ideal fashion.
The writing was on the wall for Lazio as early as the sixth minute when Emeghara put the Robur ahead.
Matteo Rubin raced down the left and his cross was met by Emeghera, who reached the ball ahead of Michael Ciani and lifted it into the roof of the net.
Lazio clearly did not learn their lesson and conceded an almost carbon copy in the 23rd minute.
This time it was the turn of Rosina to meet a left-wing cross from Rubin at the near post and lift the ball past Marchetti, with the aid of the far post.
An expected reaction from Vladimir Petkovic's men failed to materialise and Siena added a third on the hour mark.
Emeghara used his speed to get in between Giuseppe Biava and Marchetti to divert Rosina's header into the unguarded goal and complete the rout.
Lazio's response was too little and too late, with Hernanes' free-kick tipped over the crossbar by Gianluca Pegolo in the 79th minute and Ederson's effort tipped on to the top of the woodwork by the Siena goalkeeper a minute later.
Louis Saha sent a shot wide from 20 yards as Lazio failed even to get one back.