Bryan finished eagle-birdie-birdie to shoot a six-under 66 second round on Friday as Lower posted a blistering 64.
Bryan, playing on a sponsor exemption, was at 15-under 129 to set the 36-hole tournament record by two shots.
Lower had a career-best 10 birdies Friday, which tied the tournament record.
He goes into the weekend in a final pairing with Bryan and a comfortable margin over everyone chasing them.
Greyson Sigg twice ran off three birdies in a row for a 65 that left him four shots behind Bryan.
Australian Harrison Endycott shot a 70 to get to six-under, nine shots behind the leader.
In a group tied fourth at 10 under is Bill Haas, a former FedEx Cup champion who has gone nine years since his last victory.
Haas' career was slowed in 2018 when he was the passenger in a car driven by a friend, Mark Gibello, that crashed along the winding Los Angeles streets near Riviera Country Club. Gibello was killed in the crash.
Haas hasn't been quite the same, and he is hopeful of a big week to restore confidence.
Charley Hoffman, who lost in a playoff in the Phoenix Open in February, had a 68 and was also in the group tied for fourth.
Nicolai Hojgaard, who briefly had the lead Saturday in his Masters debut, came down to the Dominican Republic and will be leaving early. He missed the cut with rounds of 73-72.
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