Written by Mr. Lanthimos with Efthymis Filippou, the film is far darker than “The Lobster,” and suffused with an increasingly claustrophobic dread. Mr. Farrell adopted a monotone for the part similar to that of his “Lobster” role, but the characters’ similarity ends there.

David, his “Lobster” character, was doughy, inward, guileless and desperately lonely, all of which felt especially poignant coming from a live wire like Mr. Farrell, who said he felt great liberation in being so contained. “There was no attempt and no desire, as written, to be in any way cool, any way interesting, any way suave,” he said. But Steven, the heart surgeon he played in “Killing,” is cunning and arrogant, and by the end of the production, Mr. Farrell said, he felt very depressed.

He was drawn to the part by the same tug that drew him to “The Lobster,” finding brilliance in the twisted worlds Mr. Lanthimos creates. And in Mr. Farrell, Mr. Lanthimos said he found a true creative partner.

“It’s a gift to have that kind of relationship, it’s easier to go further and explore other things,” Mr. Lanthimos said. “This was a challenge, something more different and complex and dark, and I knew he had the understanding and tone.”

For all his work on big films, Mr. Farrell has long preferred smaller films anyway and the specific stories they can tell. When Martin McDonagh approached him to play a hit man for “In Bruges,” basically throwing him a lifeline, he almost turned down the part. He’d been in a string of bad movies and was still feeling the lingering burn of his Alexander the Great movie. (Among the sharper barbs: “He seems like a moody sad sack that I wouldn’t follow to the grocery store much less into battle.”) He worried his name might scare people away.