World number one Scottie Scheffler (27) and five-time major winner Brooks Koepka (33) are at one under, while Rory McIlroy (34) salvaged a par at the 18th to end the day at Hoylake five shots off the lead.
Lamprecht shone on his debut at the majors with a 66 after earning his place by winning the Amateur Championship at the nearby Hillside course last month.
The powerful amateur, who stands at six feet eight inches (2.03 metres) tall, used his long levers to great effect around the Royal Liverpool course on Thursday.
"I earned my spot to be here. I think the way I played today I earned to be on the top of the leaderboard, as of now," said Lamprecht.
Fleetwood, who hails from Southport, just 30 miles (48 kilometres) from the course, gave his chances of a first major title win a huge boost with a run of three consecutive birdies between the 14th and 16th.
"If you aren't going to enjoy this and these experiences, what's the point? Make sure you have the time of your life out there because it's very special," said the world number 21.
"I'm leading the Open and had cheers like that, it's really special."
Argentina's Grillo produced a stunning five-under par back nine to surge into a share of the overnight lead.
McIlroy's slow start
Back at the scene of his only British Open triumph in 2014, McIlroy got off to a slow start in his bid for a first major title in nine years.
Hs putter let him down with a shocking miss from three feet for par at the eighth to make the turn at one over.
However, back-to-back birdies at the 14th and 15th kickstarted his round before a dramatic five at the last.
McIlroy fluffed his first attempt to play out of the green-side bunker before a superb chip and putt limited the damage.
The Northern Irishman said even par was a "solid start" in tricky, windy conditions.
"It was really good in the end - these bunkers are just really tough, it doesn't seem to go into the middle of them and you're always up against the face," he told Sky Sports.
"I was quite lucky, it could have gone into a deeper part of my foot print and I'd have been there all night."
Masters champion Jon Rahm (28) was not so lucky as he paid for also finding a bunker at the 18th with a bogey that dropped the Spaniard to three over.
Scheffler got off to a flying start - two under after four holes - but the American's charge was derailed after dropping three shots in seven holes around the turn.
Little LIV impact
Defending champion Cameron Smith (29) and Koepka appear to pose the biggest threat from the group of players now regularly plying their trade in the Saudi-backed LIV Golf series.
But Smith finished at one over par after an eventful round that featured four birdies and five bogeys.
Koepka, who won his the PGA Championship in May, turned around a difficult start with three birdies in the final eight holes.
France's Antoine Rozner (30), Spaniard Adrian Otaegui (30) and American Brain Harman (36) all sit at four under.
US Open champion Wyndham Clark (29) and 2009 Open champion Stewart Cink (50) are among a five-strong group on three under.
