"Bill Gaither's Favorite Homecoming Songs and Performances" cd has "Lead Me to that Rock," but the link at allmusic.com does not specify the singing group.
The cd "Close Harmony: A history of Southern Gospel Music," also has "Lead Me to that Rock,: sung by Homeland Harmony Quartet.

The Gaither cd, "Mountain Homecoming," has "Lead Me to the Rock," public domain.

I dunno if this will help the original poster, but these and many others are listed at allmusic.com

There are 61 entries for "Lead Me to the Rock" and 21 for "Lead Me to that Rock" at that site. Are they the same song??