A three-part harmonization of a hymn seems reasonable only if it is to be sung a cappella or would be accompanied by just three (single voice) instruments. In the presence of organ (or other keyboard) accompaniment, it would suffice for members of the group to sing 3 out of the 4 parts (e.g. SAT, SAB, or STB) of a 4-part harmonization.
In my "junior choir" days, I recall singing hymns with just the SA parts of a standard SATB harmonization, sometimes even without accompaniment. It just might work in some cases to sing 3 out of the 4 parts (of a standard SATB harmonization) without accompaniment.
But, no, I don't know of any 3-part standard hymn settings.
Concordia had such a 3-part collection. Can't look now but it might have been appended to Vol. 1 of The Parish Organist. I don't recall if it was singable, the number of voices being for the comfort of beginning organists
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