Can I say: Lucky he OR him/Lucky she OR her.

Also, are they OK: I do not want to give advice to anybody AND I do not want to give anybody any advice.

Both of your sentences are correct.

I believe that technically lucky 'he' or 'she' might be correct. But, we certainly use 'him' and 'her' much more often.
In the 1956 musical Candide, they use 'o happy we', but then it has to rhyme with 'agree'.
Thank you!!!