This question comes up with some frequency. The short answer is no, but that doesn't tell the whole story.
We can do an analysis based on only the 3 indicators, then classify subjects based on this LCA, and then regress most likely class membership on the covariates and regress the distal on most likely class. But we know that this gives biased results unless you have very good classification, say entropy > 0.8.
Let's focus on the distal outcome - your continuous dependent variable. Statistically, a distal outcome acts just like another latent class indicator - conditional on latent class the indicators are independent. Statistically, the distal contributes information about the latent class variable. So why would you not want to use the distal together with the 3 indicators? The argument might be that you want to use the 3 indicators as a prediction instrument and see how well classes determined from the 3 predict the distal. But then, why not proceed as follows?
Do the analysis with the 3 indicators and the distal to get parameter estimates for how the distal relates to the latent classes. In a subsequent analysis, say using a new sample, you use the estimates from this model as fixed parameters and use information from only the 3 indicators, giving missing values for the distal. That gives you a different most likely class membership and that can be used to predict the distal using the estimates for the link between the distal and the latent class variable. That's your prediction instrument. You may find that the use of the distal sharpens your classification to be more tuned to predicting the distal. That's what happened when I analyzed the LSAY math data, predicting high school dropout.