Welcome Joko!
Paul didn't have anything to do with writing the song "Julia" - only John Lennon. If you are just going to change some of the words and sing it live to the girl, you don't need permission. You would only need permission if you were going to record it and try to sell it (permission from John Lennon's estate/Yoko Ono and also Paul since he is listed as co-writer, just like he was for "Give Peace A Chance" even though he had nothing to do with that song either!)