The 22-year-old New Zealander has taken the place of Australian Daniel Ricciardo at Red Bull-owned RB for the remainder of the season with a 2025 race seat there for the taking.
Lawson, who started at the back of the grid on Sunday due to an inherited engine penalty, had already made his mark on Saturday when he clashed with Aston Martin's double world champion Fernando Alonso in a sprint race.
The Spaniard had called him an idiot and also exchanged words with him afterwards.
"I think if you're getting into a spat and getting your elbows out with Fernando on your first race back in, you're doing alright," Horner told reporters.
"I think that he drove an exceptional race today from 19th to ninth. He was fast, he was courageous and I thought it was an excellent comeback for him."
Lawson, who made five appearances last year as a stand-in for the injured Ricciardo, said he had not expected to do so well.
"I just went for every little gap and made up some positions. We made a really good step up with the car yesterday, which we hoped would replicate in the race today and thankfully it did," he added.
Team boss Laurent Mekies said it was a great job "especially when one considers he has not raced since October last year."