。
The lovers were walking arm in arm.
Literal
Lovers [topic-は] each-other [in-に] arms [object-を] linking were-walking.
腕を組む means 'to link arms' or 'to fold one's arms' depending on context — here, with お互いに ('mutually, with each other'), it's the linking-arms reading. The て-form 組んで attaches the manner ('linking arms') to the main verb 歩いていた ('were walking'). お互いに is a fixed adverb pinning down the reciprocal sense.