Leishman shot a 10-under-par 61 to hold a three-stroke advantage after the opening round at Trinity Forest in Dallas.
Walker continued his good form from TPC Sawgrass last week as he raced to the turn in 31 and picked up further shots at 14 and 16 to get to seven under for the day, but he looked likely to card his only bogey at the 18th after a poor drive.
The 34-year-old Victorian, a three-time victor on the PGA Tour, started with an eagle on the par-5 first hole and never looked back, claiming another eagle at the 14th to go with six birdies.
Australian Marc Leishman fired a career-low 61 for a three-shot lead after the first round of the AT&T Byron Nelson at its new home in Dallas on Thursday while local favourite Jordan Spieth failed to make a move.
"It was about as easy tee to green as I've ever seen this place", Spieth said.
Leishman, whose previous TOUR low was 62, acknowledged it was one of his best rounds but couldn't match the 64 he shot in the third round of the 2015 Open Championship.
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"That's the key around here", he said.
It was largely a good day for a strong Australian contingent, with Cameron Percy (-4), Adam Scott (-4), Matt Jones (-4), Geoff Ogilvy (-2), Robert Allenby (-1) and Rod Pampling (-1) all under par. "The fairways are generous but if you are off them you are in trouble".
Marc Leishman celebrates his his birdie on the 17th hole at Trinity Forest Golf Club.
"I was hitting my irons well and played good golf", said Hataoka, who is looking for her first victory on the American LPGA tour.
Leishman was in a tie for 63rd at last week's Players Championship and he was in contention after two rounds of last month's Masters Tournament before finishing ninth, seven shots behind the victor Patrick Reed.
Two Americans, JJ Spaun and Jimmy Walker, sit on seven-under, the former carding six birdies in seven holes, but bogeying the par-four 15th.