The only sure sources to answer your question are: 1. People who are native Lithuanians who may know someone with this surname; 2. Phone book entries for the name.
I am not a native Lithuanian. The online phone book for Lithuania does not show any listing for a surname beginning DANTK-. There is a surname that comes close, namely, Dankis, which might sound a bit like Dantkus to a non-Lithuanian ear and so may have been tweaked a bit for Mr. Dankis' English-speaking neighbors. It is very uncommon, with only 4 listings in the country, all in the north in or near S^iauliai.
The ending "-o" is not typically Lithuanian, but there are few online phone book listing for folks named Dantas.
There is also the possibility that the surname was mis-transcribed where the letters "n" and "u" are often mistaken one for the other. In such a case, the name might begin DAUT-. There are listings in the phone book for the surname Daus^a (pronounced dau-shah) and Daukantas, which might be shorted in America to Daukas. There is also Daukas, again without the "t".
Prior to WWI, the vast majority of ethnic Lithuanians did not come from cities like Kaunas. But there was a province or gubernia of that same name during the Russian Empire which ruled the lands we now know as Lithuania (1795 to 1917). Immigrants often listed the province of their birth rather than the small settlement or village they were literally born in, much as one born in Angola, NY might say he was from "New York" rather than explain where exactly in the state he was from. Far and away ethnic Lithuanians were farm-based rather than town-based.