Lawson and Alonso battled during the Sprint on Saturday at the Circuit of The Americas, which led to a brief exchange afterward.
The two-time world champion felt his young rival had gone too far in their scrap and claimed he had to take action to avoid a repeat of a highspeed crash he suffered at the circuit in 2022.
They then had a brief encounter during Sunday’s race as Lawson made his way forward from 19th on the grid, a drive that ultimately resulted in points on his F1 return.
Following that initial post-Sprint exchange and an awkward moment exiting the pit lane in qualifying soon after, tensions between the two have not escalated further.
“I’m guessing he moved on,” Lawson said ahead of this weekend’s Mexico City Grand Prix.
“He didn’t fight me too hard in the race, so I guess he was obviously smart about that.
“But I don’t expect it to carry forward; no, it’s in the heat of the moment, it’s a racing situation.”
Alonso is this weekend taking part in his 400th grand prix.
The 43-year-old is, by some margin, the most experienced driver in F1 history, having started his career with Minardi in 2001.
For Lawson, competing against a driver of Alonso’s calibre and experience, was useful as he rebooted his top-flight career.
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“His race craft is very, very good, and probably one of the best in the field,” the Kiwi noted.
“And quite often [he’s been] in situations where maybe he hasn’t been in a car that’s had the pace that he’s showing it does.
“He’s always been a driver that makes that situation work. He’s been very, very good at that.
“So I think watching him for so long, I knew fighting on track that he would be a lot harder than other guys to race against.
“But I also know that he’s the type of driver you can probably trust as well with the experience he has, which is also why I raced him like I did.”
In addition to recording two points for his efforts on Sunday, Lawson also earned the praise of Christian Horner and Dr Helmut Marko.
While a boost early in his F1 return, the 22-year-old realises that he needs to continue to deliver.
“It was a really good weekend to start off, I think it was probably better than what we expected,” he reasoned.
“We made some big progress with the car over the weekend, especially on Saturday and that’s really what helps carry that pace through quali and then also in the race.
“But obviously the expectation is to carry on that performance,” he added of the feedback he’d received from Red Bull’s management.
“They’re obviously happy with how it went but this is a very different circuit, so we have to really put a lot of effort into these weekends.
“The preparation is very, very important to how we end up performing.”
This weekend, Lawson will benefit from a return to a traditional format, with three practices ahead of qualifying and the grand prix itself on Sunday.
Friday practice features an additional 30 minutes of running too, as Pirelli conducts testing ahead of 2025.
Opening practice for the Mexico City Grand Prix begins on Friday at 12:30 (local time, 05:30 AEDT Saturday).
