If my Lillie's Poke Doll was Knocked Out by my opponent, can I use Oricorio GX's "Dance of Tribute" Ability?
Yes, even though they didn't take a prize, Lillie's Poke Doll was still considered a Knock Out of one of your Pokemon.
Source: Cosmic Eclipse FAQ (2019-10-18), TPCi Rules Team (2019-10-31)

Relevant cards

Note: All applicable cards may not be listed below.
SM12_197
SM12_197
SM12_217
SM12_217
SM12_255
SM12_255
SM12_267
SM12_267
SM12_95
SM12_95