My guess is that you are computing logit utilities (an aggregate, pooled solution) within Lighthouse and then exporting the utilities to a file to take to SMRT. The problem with that is logit estimates a single vector (row) of utilities to represent the average of everybody (it's like pretending that one respondent got an awfully long survey, containing all respondent choice data). So, at that point there is indeed just one record of utilities (row) to represent the average of everybody.
To move respondent data into SMRT so that you have all respondent records and all raw choice data for each respondent (the choice task combinations each respondent saw plus their raw responses to those choice tasks) you have to export a .CHO file from Lighthouse Studio (for the choice data) and you have to export a .CSV file (containing any additional questions in the survey you want to merge into your SMRT project).
To export a .CHO from Lighthouse Studio, go to the Data Management area and add a new job. Then, click the Add button at the bottom left of the "Add Job" dialog. Choose the CBC .CHO option. Export the data (the .CHO file).
Export your other questions you want to take to SMRT also to .CSV by adding another run to that job.
In SMRT, do File + Import and use the "Choice Data (*.cho)" import type to create a new project and read in the raw CBC data (just the raw respondent answers...no utilities at this point). Then, your second step is within SMRT to choose File + Merge Variables to read in the other segmentation data.
Of course, I wonder a couple of things: why are you using aggregate logit when HB estimation (individual-level utilities) often provides more accurate and flexible answers? (I know sometimes there are reasons to want to use aggregate logit, but it is now less common to do among our users). And second, why are you wanting to use SMRT software when you can conduct market simulations within Lighthouse Studio using a more up-to-date simulation tool (I know for example that SMRT can do optimization searches that Lighthouse cannot quite do yet, so that's about the only reason I can think of).