"Luke's house" is not an official name.
Phone Calls
Luke's House is the house that Luke and his mother live in. Although the outside is never seen, the inside of the house is seen in Sue Ellen Moves In when Luke is talking on the phone and he is seen in what appears to be the living room with a picture frame in it and the walls appear to be dark green. Luke is also seen outside of a small brown house playing in the snow with Sue Ellen in the episode Arthur's Snow Biz which may or may not be his house.

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