I'm assuming you're doing either a MaxDiff or a CBC study, which you are "tricking" our software into thinking was fielded paper-and-pencil.
The approach I would think about doing would be first to follow the standard documentation for importing MaxDiff or CBC data from a .CSV file.
After the conjoint or MaxDiff data was imported and the data file created within Lighthouse Studio, I'd next want to read in the covariates variables into the data set.
I'd go to File + Data Management, then open the View/Edit Data tab. This tab acts a little bit like a spreadsheet, in the sense that you can add new columns to the data set and then paste in the data.
Another alternative is to import new variables into the dataset from .CSV file, using the Get Data tab, then selecting the Merge external data option.