Ahead of his return to Formula 1 at the US GP in Austin, Texas on October 20, the New Zealand star has exposed how Horner previously promised him a spot on the grid.
Speaking to the F1 Nation Podcast ahead of the season's climax, Lawson said: "The idea of me jumping in is something that Christian told me a year ago.
"When I stepped out of the car, that was one of the things he said to me.
"He said, ‘I give you my word I’ll basically have you in a race at some point next year’. So I always knew that was the intention and it had been talked about.
"As you know, Formula 1 is a rollercoaster and every weekend things change. It’s a bit horrible to be honest because you’re sitting there wondering what your chances are of driving and it completely depends on how the guys that are currently driving are doing.
"And you don’t obviously want somebody’s downfall to be your way in, but for me to drive somebody has to leave, obviously."