Russia's Medvedev needed just 56 minutes to subdue Lu 6-2 6-2, firing nine aces with just one double fault as he advanced to a third-round meeting with Australian Alexei Popyrin, a 6-4 6-2, winner over No.30-seed and American Reilly Opelka.
No.3 seed Alexander Zverev, ranked No.7 in the world, became the biggest upset victim so far in the prestigious ATP Masters and WTA hardcourt tournament, falling 1-6 6-3 6-1 to No.83-ranked Finn Emil Ruusuvuori.
However Medvedev, the No.1 seed in an ATP Masters event for the first time, was all over Lu from the opening game of their match.
He belted 24 winners to become the second player – along with compatriot Andrey Rublev – to reach 15 match wins this year.
Runner-up to world No.1 Novak Djokovic at the Australian Open, Medvedev ascended to No.2 in the world when he lifted the ATP trophy in Marseille.
Medvedev became the first player outside the "Big Four" of Djokovic, Roger Federer, Rafael Nadal and Andy Murray to rank No.2 in the world since Lleyton Hewitt in 2005.
But he's already looking for more.
"The only thing I feel like when you reach something you haven't done then straight away it doesn't matter and you want to go further and further," he said. "I think it's the same for everybody.
"I'm happy about my achievement but only trying to improve every day and want to go further."