。
She lives in this house by herself.
Literal
She [topic-は] alone [as-で] this house [in-に] is-living.
住んでいる is the stative-resultative use of ~ている — not progressive 'is residing right now,' but the ongoing property of being a resident. 住む always takes に, never で, because residence is a location-of-existence relationship (parallel to ある, いる) rather than the location-of-action relationship that で marks. The polite ~ています fits introducing someone's living arrangement to a third party.