Left-side 木 is the wood/tree radical, depicting a tree with branches above and roots below. It indexes 楼 in the family of wooden constructions — multi-storey buildings in pre-modern China were timber-framed, so the radical is materially exact. Same family as 桥 (bridge), 棚 (shed), 柱 (pillar), 板 (plank).
Right-side 娄 supplies the sound (lóu → lóu, identical). 娄 (simplified from 婁) carries a faint sense of 'hollow/repeating' that resonates with the stacked-empty-rooms image of a multi-storey building, but the active role is phonetic. Same right side in 数 and 搂 (hug).
