Which image compression is better, LZW or ZIP? I am using Lightroom to export images.
Better is a relative term and, to some degree, will vary in terms of amount between the two depending on a variety of factors including the bit-depth, frequency of discrete colours, etc. Some experimentation may be necessary on this front, though my reading indicates LZW is good for lower bit-depth images with lots of the same colours and tones in it and ZIP for when that is not the case. In other words, if the image is 8 bits go LZW and if it is 16 bits go with ZIP, as a rule of thumb, but with the caveat that it's not an absolute rule and there may be exceptions.
The only other thing I'd note is that LZW has been in the TIFF standard since 1992 and ZIP since 2002 (as part of a supplement when Adobe added it). While that's probably more than enough time for it to no longer be an issue, there may be the odd piece of software out there that handles LZW compression but not ZIP.