It seems the Catholic church in Latvia is an extraordinary success story.
The Baltic state Latvia received Christianity primarily from the Latin West under the influence of German crusaders.
After this initial crusading period the control of the lands we know as Latvia today were divided for long periods under different ruling parties: First the Livonian brotherhood (a German order much like the Teutonic knights) eventually the Order of knights broke up, German dukes controlled the south and Swedes acquired the north for a time. Under these conditions most of Latvia became Lutheran during the reformation and Catholic priests were eliminated wherever possible.
The southern part of Latvia was called Courland and at one time became constituted a part of the Commonwealth of Poland, yet retained the German dukes and landlords as well as the Lutheran religion among the ruling class. Some of the leading German families may have become Catholic again during that era (1561-1795), I wouldn’t know but I saw a list of the dukes somewhere that listed one with a middle name of Casimir, the name of a Polish Catholic saint and a hint of possible religious affiliation. This political situation continued until the Duchy of Courland went to Russia at the third partition of Poland.
Therefore I think that any Catholics in Latvia would be of the Latin Catholic church Sui Iuris. It is also possible that the family of this person originated near the southern border with Lithuania in Courland. If they have not recently converted to Catholicism the family might trace their religious affiliation back to the time when Courland was politically linked to Poland. If they retained their Catholicism from the period before the reformation it would be extraordinary, though not impossible.
The Lutheran church and Russian Orthodox church have not fared as well as the Catholic church through the Communist era and the Latin
Catholic church continues to grow. After I bagan to write this post I found a site that explained it well, so I linked it in.
Also any presence of Byzantine Christians in the area would most likely be Orthodox from the time after Russia absorbed the country. If, against all odds they were actually Byzantine Catholic they would probably actually be a unique church Sui Iuris deriving from the Russian tradition, but I doubt that a hierarchy was ever established for Latvian Eastern Catholics and they would be a very, very tiny group if they existed at all. One last remote possibility is that some Ukrainian Greek Catholics migrated to the area after WWII because the Soviet Union absorbed both western Ukraine and Latvia at the same time. But such people would not have forgotten that their families originated in Ukraine after such a short period.
