She lives in London.

Literal

[topic-は] London [in-に] is-living.

住む ('to reside') uses the locational に for one's place of residence — distinct from で, which would mark the location of an action, not a state. Pairing 住む with ~ている produces the standard way to say 'lives in' in Japanese — note that 住む alone (住みます/住んだ) is rarely used for current residence, since living somewhere is a state, not a one-off action.