It was in the 90s, especially after the Dr Dobbs article about it, and tons of late 90s and early 2000s games, like Grim Fandango, Baldurs Gate and Escape from Monkey Island used Lua due to its hotness.
Actually, Grim Fandango was the very first known game to use Lua and wasn't due to any hotness. Bret Mogilefsky, who against skepticism, dared to try to create a new scripting engine to replace the aging SCUMM engine. He was given the Dr. Dobbs article by a colleague and things came together. After the technical success of Grim Fandango, it was applied to Escape from Monkey Island.
A few years(?) later at GDC, there was a 2 hour session to discuss scripting in games. Near the end, after everybody was depressed with no viable solutions, Bret's colleague exclaimed, "Or you can do what Bret did" and he was dragged up on stage. Bret gave an impromptu spiel about what Lua was and how they used it at LucasArts. Everybody else frantically scribbled down notes and that was how the video game industry adopted Lua as the dominant game scripting language.
*Source: Bret Mogilefsky's talk at the very first Lua Workshop in 2005
A few years(?) later at GDC, there was a 2 hour session to discuss scripting in games. Near the end, after everybody was depressed with no viable solutions, Bret's colleague exclaimed, "Or you can do what Bret did" and he was dragged up on stage. Bret gave an impromptu spiel about what Lua was and how they used it at LucasArts. Everybody else frantically scribbled down notes and that was how the video game industry adopted Lua as the dominant game scripting language.
*Source: Bret Mogilefsky's talk at the very first Lua Workshop in 2005