Lawson, who had set the fifth fastest time in the first qualifying session, missed making the top 10 for the third session by just 0.122 seconds, and for the second time in as many days had a lap deleted for racing too wide.
The Racing Bulls driver was also under fire from Red Bull driver Yuki Tsunoda, who accused him of deliberately slowing down in front of him.
Tsunoda's Red Bull teammate Max Verstappen took pole position for tomorrow's grand prix, finishing fastest in the third qualifying session after winning the sprint race.
The second session was a comedown for Lawson, after doing so well in the first and coming ninth in the sprint race.
Tsunoda, who replaced Lawson in the senior Red Bull team early in the season, finished 13th in the second qualifying session.
"Lawson is, uh, disturbing me on purpose, like slowing down like hell in corners," Tsunoda alleged on his team radio.
His engineer replied: "Yeah, we saw that in Turn 11."
When asked about Tsunoda's comments, Lawson said to reporters: "What, me?
"I have absolutely no idea what he's talking about.
"Traffic is always a little bit tough around here. This weekend, it's been something that we've all been dealing with.
"We got hit really bad yesterday in sector one. I can't possibly think where I could have been in front of him - it's just one of those things."
Lawson said his second session had been ruined by a gust of wind.
"We had a very fast car, we just got hit by a massive gust of wind at the start of the lap," he said. "From there, you're trying to make up lap time, so it sucks.
"The car has been is very, very quick. Unfortunately, it's cost us quite a lot of lap time."
In the sprint race, Lawson started from 15th and after avoiding trouble from a crash on the first lap he drove aggressively to finish 10th, before being elevated to ninth after the race when Ollie Bearman, who finished eighth, was hit with a 10-second time penalty.
Lawson's Racing Bulls teammate Isack Hadjar crashed into a wall during the first qualifying session. He wasn't injured but showed his frustration on exiting the car.
Verstappen beats Norris for pole
In the final qualifying session, four-times world champion Verstappen beat McLaren's Lando Norris for the top slot.
Norris had crashed out of the sprint after a collision with teammate Oscar Piastri that saw the championship's top two retire without scoring, Reuters reported.
Ferrari's Charles Leclerc qualified third fastest and shares the second row with Mercedes' George Russell, winner of the previous round in Singapore, while Piastri will start from sixth.
The Australian is 22 points clear of teammate Norris, and 55 ahead of Verstappen, ahead of Monday's race at the Circuit of the Americas but risks having his margin slashed.
Verstappen's bid for a fifth successive title, once dismissed as impossible, is gaining strength after he also won the Saturday sprint race from pole position while both McLarens crashed out.
Ferrari's Charles Leclerc, last year's winner in Austin, qualified third fastest and shares the second row with Mercedes' George Russell, winner of the previous round in Singapore.
Verstappen needed only one flying lap to secure his seventh pole of the season, the Dutch driver failing to make it around in time for a second attempt in the final phase, but he was still nearly three tenths faster than Norris.
"Unfortunately I couldn't do my final run. It was a bit messy with the out-laps, but luckily, we didn't need it," Verstappen said.
Norris, who took pole last year, said he could not have done better.
"We were pushing and I'm still happy with P2. It could have been worse, But there was no chance we could have got on pole today," said the Briton.
"I look forward to hopefully having a good race with Max. We have had some good ones in the past, so looking forward to it again."
Ferrari's seven times world champion Lewis Hamilton qualified fifth and shared the third row with Piastri, while Mercedes' Kimi Antonelli lined up seventh and Haas's Oliver Bearman eighth.
Carlos Sainz was ninth fastest for Williams and Fernando Alonso completed the top 10 for Aston Martin.
- Additional reporting RNZ and Allied Media
