Performace of Fischer projection as dimension reduction compared to other LDA methods
I didn't get what you meant by "other LDA Methods". To the best of my knowledge, Fisher method is just one.

Sklearn has the implementation and you can find it here.

Is it good or bad? When it comes to dimensionality reduction you don't know as dimensionality reduction methods are usually unsupervised. So if PCA works better? No one knows. At least in the context of two-class classification, Fisher method is still brilliant.

Hope it helped!