Fourth seed Kei Nishikori of Japan beat American Steve Johnson 6-1 7-6 (4) and Colombian Alejandro Falla ousted home player Peter Gojowczyk 7-6 (4) 7-6 (2).
Seventeen-times grand slam champion Federer made up for the walkover by continuing his preparations for Wimbledon with an exhibition match against Germany's Christopher Kas who is ranked 78th in doubles.
Lu joked: "If I'm 150 percent and he's 100 percent I think I'd still lose".
Six-times Halle winner Federer now faces Nishikori in the semi-finals.
Brown captured the imagination of the crowd on Thursday with a convincing win over world number one Nadal but failed to match that form as he lost a marathon match against Kohlschreiber.
The wildcard looked on course for another victory, leading 5-2 in the tiebreak, but the German number two kept his cool to save five match points and secure a meeting with Falla.
"I don't think a third set ever went so long," said 2011 winner Kohlschreiber. "Absolute war of nerves.
"It was very exhausting to keep calm, stay cool and maybe even enjoy it. The atmosphere was incredible but in the end you just want to leave the court as the winner."
(Reporting by Tom Hayward, editing by Tony Jimenez)
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