"Lost Lucas" is one of the Quests found in OMORI.
It is a quest found in Faraway Town and is completely optional. This quest has to be done after completing Kel's errands but before ending the second day.
The Artist's dog, Lucas, has gone missing, now it's up to Sunny and his friends to find him.
To solve this quest, simply walk to Kel's house and interact with Lucas there, now go back to the Artist.
This quest rewards the player with the paintbrush.