Question about gauge

Neitrino

If I have a theory... some Lagrangian and I need to impose a gauge condition... what is more preferable

1) The subject gauge naturally arises from the structure/type of the lagnagian
(Like a Lorentz gauge that can automaticaly arise in Electrodynamics)

2) Or I have just to impose it "rigidly" even if I cant get it from the theory.
(suppose I added some terms to vector field lagrangian and can not get Lorentz gauge by taking divergence of equation of motion as used to do in conventional case, but I need some gauge to reduce degrees of freedom.... I if impose my Lorentz gauge "rigidly" will it be acceptable)

If I am not cler with my question please tell me and I will try to be more clear