Not every repetition qualifies as luzūm mā lā yalzam. A sound correspondence already required by the definition of the rhyme or sajʿ is not an added condition.
Agreement in the rawī is foundational; the further question is what nonrequired pre-rawī feature the speaker has also kept the same.
Nor does simply repeating the same word prove this device. One must identify the location of the commitment, show that it is optional relative to rhyme, and consider whether it fits the meaning.