In MINPAR block of the Input file, I declared:
{{5},{Min->-1,Max->1}} (*L0INPUT*),
and I don't want L0 to pass the value 0.
Is it possible?

Hi,

no, there is no way to exclude 0. However, exactly 0 will most likely also never be chosen, but there will always be some numerical deviation from it.

Cheers,
Florian