She's in the middle of eating lunch.

Literal

She [topic-は] lunch [object-を] eating [in the middle of-ところだ].

~ているところだ ('is in the middle of doing X') captures a snapshot of an action in progress — right at this moment, she's eating. It's more emphatic about the 'right now' timing than plain ~ている. ところ literally means 'place/point' but here refers to a point in time.