Is it correct to say
alive once alive forever
meaning one who feels alive once lives forever?
It's obviously not a sentence. However, it is structured exactly the way that mottoes and such are generally structured in English. Some would prefer a comma in it:
Alive once, alive forever
And that does reinforce the structure as two parallel adjective-adverb pairs.
So yes, it works as a motto or saying, and if you clarify the structure with a comma I think native speakers will reliably understand it the way you present it. Just don't mistake this for it actually being a valid sentence. Titles, headings, sayings and the like don't have to follow the normal rules.