Both Morkus and Morkevic^ius are found in the online found book for Lithuania and are spelled using today's Lithuanian rules. Morkus is not an Americanized version of the name, though some immigrants to the U.S. named Morkevic^ius might have shortened it to Morkus. The ending "-vic^ius", a Lithuanianized form of the Polish ending "-wicz", means "descendant or sone of someone named Mark", so the shorter form is probably the older one.
Names do not have ethnicity, only people do. Names can be spelled using various languages. For example, Vilnius is the Lithuanian version of the city name which to Russians is Vilna, to Poles, Wilno, to Germans, Wilna. So the surname Morkevic^ius might well be spelled Markowicz in a Slavic tongue.
The letter "j" in Lithuanian is pronounced like the letter "y" in the English word "yellow" so it is common for names beginning with "j" in Lithuanian to become a phonetic "y" in English. The ending "-ski" is the Polish ending for the Lithuanian "-skas," "-skis," or "-skys."
"Ayragola" is most likely Ariogala in the Raseiniai district, northwest of the city of Kaunas.