Games like Lume
Games like Lume include The Room, There Is No Game: Wrong Dimension, Gorogoa, Morphopolis, and Florence. We matched them by the tags players give Lume on Steam (Adventure, Indie, Point & Click, Casual, and Puzzle): closest matches first, and among equally close ones the better-known games.

The Room
Shared: Point & Click · Puzzle · Adventure

There Is No Game: Wrong Dimension
Shared: Indie · Adventure · Point & Click

Gorogoa
Shared: Indie · Puzzle · Casual

Morphopolis
Shared: Indie · Puzzle · Point & Click

Florence
Shared: Indie · Adventure · Casual

Chants of Sennaar
Shared: Adventure · Indie · Puzzle

Samsara Room
Shared: Indie · Adventure · Puzzle

Assemble with Care
Shared: Indie · Casual · Puzzle

The Room Two
Shared: Point & Click · Puzzle · Adventure

Broken Age
Shared: Adventure · Point & Click · Indie

Donut County
Shared: Indie · Casual · Adventure

Gomo
Shared: Adventure · Indie · Point & Click

The White Door
Shared: Adventure · Indie · Point & Click

Iris.Fall
Shared: Adventure · Indie · Casual

Little Inferno
Shared: Indie · Casual · Puzzle

Silence
Shared: Adventure · Point & Click · Indie

The Room Three
Shared: Adventure · Puzzle · Point & Click

Plug & Play
Shared: Indie · Casual · Short

Fran Bow
Shared: Point & Click · Adventure · Puzzle

Journey of a Roach
Shared: Adventure · Indie · Point & Click

Zup! 2
Shared: Indie · Casual · Puzzle

Monument Valley
Shared: Adventure · Puzzle · Casual

Contrast
Shared: Indie · Adventure · Female Protagonist

Syberia
Shared: Adventure · Point & Click · Puzzle