Are there general rules for the maximum number of variables within a latent class analysis compared to the total amount of subjects and number of classes? We have only 104 subjects, but we can go up to 27 variables which seems a bit much to me. Is using factor loadings in an EFA a possible way to eliminate variables (if necessary)? Are there any references in scientific articles on this issue?
You should have at least as many subjects as variables or parameters in your model. Short of that, you could do a simulation study to determine the number of subjects needed.
LCA like EFA is an exploratory analysis and the set of variables should be constructed for the analysis. It should not be just any set of variables. I would decide on the variables based on this not the number of variables available. I don't know of any references that deal with this.