。
She lives in luxury.
Literal
She [topic-は] luxuriously is-living.
ぜいたく (贅沢) is a na-adjective/noun for 'luxury / extravagance' — both as material excess and as the sense of 'a luxury one shouldn't take for granted' (e.g. ぜいたくな悩み, 'a luxury problem'). The adverbial form ぜいたくに ('luxuriously') modifies the verb. 暮らす and 住む both translate as 'live', but they pull apart: 住む points at the location ('reside'), 暮らす points at the lifestyle and daily existence ('live one's life'). With an adverb of manner like this, 暮らす is the right choice — it's about how she's living, not where.