Levy made par on the ninth hole to complete a second-round 63 and remain on 17 under par.
Sweden's Michael Jonzon carded a third-round 63 to reach 13 under, one ahead of Briton Ross Fisher.
German Martin Kaymer, preparing for next week's Ryder Cup, was tied fourth on 11 under after a second-round 64 with Belgian Thomas Pieters on four under ahead of his first appearance for Europe in the biennial match against the United States.
(Reporting by Ed Osmond, editing by Alan Baldwin)
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