Champions Juve moved on to 56 points from 21 games after Spanish centre forward Llorente scored with a looping header on the hour to cancel out Antonio Candreva's 27th minute penalty.
The spot kick was given after goalkeeper Gianluigi Buffon was sent off for crashing into Miroslav Klose just as the striker had nipped the ball around the Juventus captain.
Lazio stay ninth on 28 points and continue their unbeaten run under new coach Edy Reja, who has seen his side gain eight points from four games since returning to the dugout as the replacement for Vladimir Petkovic after the winter break.
The Rome side were unlucky not to win after striking the woodwork twice in the second half, first through a Klose header that keeper Marco Storari pushed on to the bar and then through Keita Balde Diao's 86th minute curling, long range strike that rebounded off the post and back into Storari's arms.
The draw means Antonio Conte's Juve side have widened the gap on second-placed AS Roma, who have 47 points and face a tricky trip to surprise package Hellas Verona on Sunday (1130
GMT).
Earlier, third-placed Napoli left their feint title hopes hanging by a thread after a late Raul Albiol goal salvaged a 1-1 draw at home to struggling Chievo to put them on 44 points.
(Reporting by Terry Daley; Editing by Ken Ferris)
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