So... is Koi to Uso finished or not?
NO, it is not finished.
Why?
The anime finished before the manga:
Anime finished: September 19, 2017
Manga finished: January 07, 2022
MangaUpdates contains information about the anime adaptation and indicates that it is incomplete.
Watching Order (by release date)
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Synopsis
Koi to Uso presents a society where the Japanese government assigns marriage partners to its citizens based on scientific compatibility.
The story follows Yukari Nejima, an average teenager who unexpectedly confesses his love to his crush, Misaki Takasaki, and is surprised when she returns his affections.
However, his romantic hopes are complicated when he receives his government-assigned marriage partner notice, throwing his personal desires into conflict with societal expectations.
His assigned partner, Ririna Sanada, becomes intrigued by his forbidden romance with Misaki, adding another layer of complexity to Yukari's already confusing situation. He must navigate a world where love and societal rules clash, facing difficult choices about his future.