I am Greek and familiar with the poem, and I can say that Sumelic and Scott are right to interpret this as a misunderstanding of Byron. Ζωή μου means indeed My life, while Ζώη μου means nothing at all,...
Nothing; all it might do is tell the reader to make a slight pause between the two lines.
The original 1840 punctuation was:
Не вмре, не загыне:
Отъ де, люды, наша слава,
Слава Украины, —
But within ...