She lives in London now.

Literal

She [topic-は] now London [in-に] is-living.

住む ('to take up residence') always appears in the ~ている form when expressing 'to live (in a place)' — the bare verb 住む describes the act of moving in or settling down, not the ongoing state of residing. The location of residence takes に, not で: residence is treated as existence in a place. London (ロンドン) is one of the most familiar Western city names in Japanese, anchoring sentences about study abroad, travel, or expat life.