Does that mean the Latent Class segmentation can only be done once a conjoint/maxdiff study is carried out?

Answer 1

I believe it just means, you can do it but with your own toolset/solutions. There is no automated tool to do it for you.

Answer 2

No.  You can use Latent Class for any logit-based data.  It simply is a matter of writing a script that can convert your data to the .cho or .chs layout.  You should be able to export your data from SPSS to a .csv file, and then run a script on that.