There are various synonyms that can be used to describe the phrase "overtaken by lust." Some of these synonyms might include infatuated, smitten, consumed with desire, or enraptured. Other options might include besotted, love-struck, head over heels, or captivated. Each of these synonyms conveys the same general meaning as the original phrase, but with slightly different nuances and connotations. Depending on the context in which they are used, some of these synonyms might be more appropriate than others. Ultimately, the choice of which synonym to use will depend on the specific situation, the intended audience, and the desired tone.