If you want to find out what characteristics, outside the conjoint analysis, best predict whether they're in group 1 or 2 you can run a supervised data mining model.
First, use the discrete segment assignment variable that's output by the LC software (not the probabilistic assignment to each segment). Now use that variable as the dependent variable and run a discriminant analysis using other variables to predict the group membership variable. Alternatively, use that segment assignment as the dependent variable in a logit model and use other variables as predictors. Alternatively, predict the dependent variable using a tree-based model (I use R for this, as it has several excellent tree models available - for your case I would probably start with rpart and build a classification tree). I usually try all three of these methods to help me identify the significant predictors. In my experience I probably end up with discrim as the best predictive model half the time, logit maybe 10% of the time and a tree the remaining 40% of the time.
If you wanted to get really fancy you could use the % likelihood of each respondent being in each model and use an allocation-based logit model to find the best predictors (I do this very infrequently - it's a bit more work and I haven't seen better quality results).
