You need to deal with the continuous variable(s) upstream within the coding of the design matrix.
I'd export the raw CBC data (the design info and the respondents' choices) to a .CSV file (using the File + Data Management + Export Data + Add Job... + Add + CBC (.CSV)) functionality. Then, I'd follow the instructions in the Sawtooth Software Standalone Latent Class manual (in Appendix C) for modifying the exported .CSV file to create continuous variables for prices. For one version of the .CSV file, I'd collapse the two price attributes into a single attribute and make the collapsed attribute a continuous price variable. The other .CSV has price for cars as two continuous variables.
For the purpose of the 2 log-likelihood test, when running the model in our Latent Class standalone software (not Lighthouse Studio, but the standalone version of Latent Class that you can install from our website), I'd tell it to run a 1-group solution (equivalent to aggregate logit). Specify that the price variable(s) are to be "user-specified" rather than the default part-worth. Run it on the first .CSV file so that price for cars is just a single continuous variable. Then, run it on the second .CSV file so that price for cars is two continuous variables.
Compare the log-likelihood fit between the models. Multiply that difference by 2. This result is distributed as chi-square. Since one model adds just one parameter compared to the other model, the DF=1 for the chi-square test.