The two teams are separated by eight points, with a further five to Alpine in sixth in the constructors’ championship.
RB had sat sixth for much of the year, only to be overhauled by Haas in recent races and a surprise double-podium saw Alpine leapfrog the pair of them.
With prize money paid out against the constructors’ championship placings, it’s a battle that’s potentially worth millions to the team next season.
Haas ended the day with the upper hand, Nico Hulkenberg third fastest in Free Practice 2 while team-mate Kevin Magnussen was eighth.
Yuki Tsunoda was the best-placed RB driver in 10th, though only 0.006s faster than Lawson in 11th.
“It’s so close, like the midfield right now,” Lawson said.
“One-tenth up and we’re P8 or something like that, and then one-tenth back and we’re P16.
“It’s very, very close.”
Magnussen’s best was a 1:24.235s. By comparison Lawson logged a 1:24.503s.
From Hulkenberg in third to Jack Doohan in 19th, the field was covered by less than a second.
Still, RB has work to do if it is to reel in Haas, a car Lawson suggests has had the edge over his own in recent events.
“In Qatar he kept a Red Bull behind in the race,” the Kiwi said of Hulkenberg’s recent form.
“They’ve been strong a lot recently.
“Unfortunately, the edge we maybe had on them earlier in the season is maybe gone, and it’s probably going to be a bit of a dog fight this weekend.”
Encouragingly, it was a better start in Abu Dhabi than RB experienced a week ago in Qatar.
It was a dismal weekend is Losail for both Tsunoda and Lawson, the pair the last two home on the lead lap in 13th and 14th respectively.
“Right now, we’re in a good place,” Lawson ventured.
“Obviously, we’re chipping away, but so is everybody else.
“Compared to last week, we’re hopefully in a stronger position.
“We did feel more confident coming here, I would say, with the car.
“But at the same time, we’re not exactly where we want to be.
“We’ve Haas with Nico, I think he was fourth in that session, third in that session… We obviously need to try and bridge that gap.
“But it’s a strong start.”