Does anyone know if image quality is exact the same of a zipped TIF vs. a non-zipped ditto?
Is it a lossless compression like LZW ?

Lossless...

By "Lossless..." - do you mean that LZW-cpmpression isn't lossless??

I am asking because my customer wants me to zip my tif files before transmitting via FTP.
I never use any compression of tif because in my eyes any compression means throwing out image data from the original file.
But what is the fact here... am I right that any compression method affect image quality and has to be avoided for maximum possible image quality?

It is lossless compression. You lose nothing other than file size.