Dunno about the interpretation but I found this, FWIW:
The Latin phrase that appears on the Hat Creek Cattle Company sign in "Lonesome Dove" is a garbled corruption, and there's no direct translation. It derives from the scholia to Juvenal 2.81 which cites the proverb "uva uvam videndo varia fit" This means something like "a grape changes color [i.e., ripens] when it sees [another] grape"
Novelist Larry McMurtry probably intentionally misused the Latin, perhaps to make a point about Augustus McCrae's tenuous understanding of the language.
From there, any number of interpretations have arisen to explain why McMurtry chose to communicate that particular idea. Probably the soundest theory is that the phrase serves as a metaphor for the group's journey, as many of the story's characters go through a process of personal maturation and development. Much like grapes ripen in the presence of others.