Well, it's just a guess, it could be something different (thats why I've inquired about your pronunciation).
I have checked Lithuania's Surnames Dictionary:
Aidukavičius - Ai (like I) duk (like dook)/ av (like av(enue)/ ič (like itch)/ -ius(like name (Dar)ius)
Eidukevičius - Ei (like Ey! or a(te))/ duk (like dook)/ ev (like ehv)/
There were more of such surnames.
As you can see, lithuanian-english vowel pronunciatio/spelling is rather different.