The phrase "lie embedded" can be replaced with a variety of synonyms, each of which conveys a slightly different nuance. To suggest that something is deeply ingrained or rooted, one might use "entrenched" or "fixed." Alternatively, one might evoke a sense of secrecy or concealment by saying that something is "hidden" or "veiled." For a more ominous or portentous effect, "lodged" or "implanted" suggests something that is difficult to remove or overcome. Ultimately, the choice of synonym will depend on the context in which the phrase is being used, as well as the tone and emphasis of the surrounding text.