Leisure Suit Larry predates Linux by quite a bit (as I recall the first 8-bit versions of the game came out in the early 80s). As for Unix, in the olden days there were a lot of Unix variations (so there was a tendency to refer to ix as a generic term for all the variations) running on any platform that was at least 16-bit (I don’t think* there were ever any 8-bit Unix variations, but I could be wrong).
Huh, I was pretty sure that it was out while I was in high school so before 1986, but I guess that must have been some other adult video game paving the way for LSL.
Maybe you were thinking of Softporn Adventure from 1981. It's a text adventure game by Sierra (at the time they were called On-Line Systems), and Leisure Suit Larry 1 is a graphical adaption of it. Source Wikipedia.