Do you suppose there were two Lutheran Churches, or could this be the same one?Info from TX Handbook:
RHEA, TEXAS. Rhea is in northwestern Parmer County. It was named for the brothers Joe E. and John W. Rhea, who developed a ranch on former XIT Ranchqv land in July 1901. In 1906 the Rheas sold out and moved to Roswell, New Mexico. Two years later, however, Herman F. Reinking purchased a section of the Rheas' land and brought in several German Lutheran farmers from his home state of Indiana. They quickly established a school and a church, around which grew a close-knit community. A post office was opened in 1909. Over the next several years these settlers endured the droughts, water shortages, and occasional blizzards the plains had to offer and adopted new farming techniques. The Rhea school was a focal point of many community gatherings until 1949, when the district was partitioned between Friona and Bovina. Nevertheless the Immanuel Lutheran Church and adjacent parish hall remain the community nucleus, especially on Sundays and holidays. The Sherley grain elevator, a grocery and feed store, a veterinary clinic, an engine service, and an auction service are also available to area farmers and ranchers. In 1980 Rhea reported a population of ninety-eight. Since 1924 mail has been routed through Friona.
Sounds like the church was there as late as 1980.Try the Parmer Co, TX GenWeb site.Click on Volunteer Lookups.One person has a couple books they will check -- maybe she canhelp with information on the church.If nothing else she might be able to pass you along to a local historical society or public library.