What scale does LightGBM use for output?
The underlying model will be a stepwise function. I don't see any garanty that it will work better (or worse) with the transformation, in the general case. This may be different depending on you variable (for binary variables you may want to work directly on the linear predictor). 

However, in practice, if you know there is an underlying link transformation, I would suggest you to use it. This will often ease the model intepretation.