If you combine the two data files into a single file (e.g. export the two .cho files and concatenate them, making sure to group together the observations for a given respondent) then the LC analysis would run and would help you group respondents. I might want to think it through first, but if you want to take into account that your two DVs are different, you might want to pretend for the purposes of this combined model that you have twice as many predictors as you do - the attributes as they predict uniqueness and then the same attributes as they predict needs.