Lux's taunt about power levels is a reference to the manga/anime Dragon Ball Z.
Lux's taunt "In the name of Demacia, I will punish you!", is likely a reference to the manga/anime Sailor Moon.
Lux's movement quote "I love it when a plan comes together" is a reference to the A-Team's Colonel Hannibal Smith's favorite catchphrase.
Lux's joke "Shhh! I'm charging my laser..." is likely a combination reference to a flash video meme which starred Imperfect Cell, a villain from Dragon Ball Z, where he said "Imma firin' mah Lazer". It could also be a reference to Lady Jaina Proudmoore from the Warcraft series. Lady Jaina Proudmoore often says Shh, I'm trying to think here.'.
Lux's joke "Double Rainbow? What does it mean?..." and the follow up joke "Well, a 'double rainbow'..." is a reference to a YouTube video where a man severely overreacts to seeing a double rainbow.
In the polish client, Lux's joke "Light? I carry it in myself" is a reference to a line from a polish song "Light, you carry it in yourself" and is sung in the same melody.
The splash art for Sorceress Lux resembles the character Marisa Kirisame from the Touhou Project, when Marisa is shown in her navy-blue dress and riding a broom (or a vine) in memorable versions. Also in the splash-art of the Sorceress skin, Lux is in front of a full-moon, likely a reference to Touhou 8 (Imperishable Night), the first game in the series to have clearly depicted Marisa on a broom, where the story revolved around retrieving stolen full-moon.
Spellthief Lux is another reference to Marisa Kirisame, who also steals spells.
Imperial Lux is likely a homage to the Star Wars universe; bearing a strong similarity to Admiral Dodonna of the Old Republic.
Imperial Lux is often compared to the visual look of Street Fighter's M. Bison who has a fairly similar appearance.