I hope your fixed design was created in a way that will support efficient utility estimation...I'm assuming so for the following suggestions.
One way to fool the software into doing this is to make a new study in Lighthouse Studio for the purposes of analyzing your CBC data. Enter your attributes and levels again exactly as you had them in the original study. And, the same number of choice tasks, number of concepts per task, etc.
In that new Lighthouse project, generate a new design (say, balanced overlap) with as many versions as your original fixed design (presumably 1). From the Design tab, click the Export button to export the design to a .CSV. Replace the design Lighthouse just generated with your design from the original study (you can export that original design to a .CSV file so you can just paste the info out of it into the new .CSV file). Import the modified .CSV design file into the new Lighthouse project (using the Import button from the Design tab), so now you have your fixed design represented within "Random" CBC tasks.
From the original project, export the responses to the original fixed tasks to a .CSV file. Format these for paper-and-pencil import with the new project. In the new project, use Field + Create Accumulate Data Template File. That gives you a .CSV with just header rows in it. That's the starting point for pasting the raw respondent answers to the choice tasks into. In the new project, use Field + Accumulate Paper & Pencil Data to read the "paper and pencil" data from the .CSV file into the new Lighthouse project. That should be it. You may need to copy other segmentation data from your original study into this new one if you need them for segmentation, covariates, or weights.
Perhaps somebody else has a better trick for doing this, but it's an approach that will do it.