This is a very general reply, but typically it would be good to have theory-based idea on what variables you want to put in cluster analysis instead of deciding that on the basis of whether the model works or some other post-analysis statistical criterion. But in my understanding it's fairly typical to form the classes (i.e. run the LCA) based on some somewhat coherent group of variables (such as shopping habits) and then investigate cluster membership's relations with other variables (such as demographics) in a further analysis (e.g. chi-square tests or some form of regression). Whether this is a good idea is a very broad question that requires subject knowledge and knowledge about the particular research questions and goals of the study.

This is a very general reply, but typically it would be good to have theory-based idea on what variables you want to put in cluster analysis instead of deciding that on the basis of whether the model works or some other post-analysis statistical criterion. But in my understanding it's fairly common to form the classes (i.e. run the LCA) based on some somewhat coherent group of variables (such as shopping habits) and then investigate cluster membership's relations with other variables (such as demographics) in a further analysis (e.g. chi-square tests or some form of regression). Whether this is a good idea is a very broad question that requires subject knowledge and knowledge about the particular research questions and goals of the study.