The problem with both spellings is that they are not Lithuanian. No name in Lithuanian ends in "-un". However, German names often do, so I suspect that the Lithuanian name has been "Germanized", just as S^iauliai is Schaulen in German. Most surnames in Lithuanian have the following endings: "-as" or "-a", "-is" or "-ys", and "-us". Some Russian or other Slavic names can be found today in Lithuania that do not comport with the typical endings, even though the folks are citizens of Lithuania. It is also possible that they were ethnic Germans who lived in Lithuania.
Also, the spelling "Diczun" has that Polish "-cz-" in the middle of it. Lithuanian has only two letters "c", one with a little birdie over it (typed "c^" on non-Baltic keyboards), and one without. The "c" with the birdie is pronounced "ch" as in the English word "church." The other "c" is pronounced "ts" as in the English word "hats." The sound of "c" in English in the word "center" is represented by the letter "s" in Lithuanian. The sound of "ch" in the word "cloud" is represented by the letter "k" in Lithuanian.
So assuming the root or stem of the name is correctly spelled "Dicz-" it would have to be pronounced "ditsz-". If it is spelled "Dic^z-" then it would sound like "dichz-".
My hunch is that it was originally something like Diksas (pronounced DIK-sahs), Diks^as (pronounced DIK-shahs) or even Diksa (pronounced DIK-sah). It could also be Dikc^ius (pronounced DIK-choos). But presumably, you've heard the name pronounced and thus, with the above information, you can probably re-construct its original spelling, at least the root of the name. There are other possible spellings as well, so if you could find an early record of some kind with the name as originally written and spoken, such as their birth or marriage certificate (you'd have to know the year of their birth and the village name), your problem would come much closer to being solved.
Perhaps your grandfather served in the U.S. Army during WWII. If so, his military record would likely be helpful. Likewise if he became a citizen, his naturalization records would help. Have you tried any of these?