The Merseyside outfit got the better of their Premier League rivals 2-0 at home in the quarter-finals of the FA Cup.
Lukaku scored both the goals for Everton at Goodison Park, first in the 77th minute and then on 82 minutes.
Chelsea ended the game with 10 men due to the dismissal of Diego Costa in the 84th minute.
Everton also failed to finish the tie with 11 players, as Gareth Barry was dismissed on 87 minutes.
Lukaku and Lennon have taken to Twitter to revel in the win against Chelsea.
I'm so happy for the team! Such a great performance! Thanks for the messages aswell! God bless! pic.twitter.com/NQb9s5POcT— R.Lukaku Bolingoli10 (@RomeluLukaku9) March 12, 2016
What a win that was!!! The atmosphere was unreal today,,next stop Wembley #Toffees— Aaron Lennon (@AaronLennon12) March 12, 2016
Over the course of the 90 minutes at Goodison Park on Saturday evening, hosts Everton had 43% of the possession, took eight shots of which four were on target, and earned five corners.
Visitors Chelsea had 57% of the possession, took five shots of which one was on target, and earned two corners.