Understanding the mechanism that connects heat transport with crystal structures and order/disorder phenomena is crucial to develop materials with ultralow thermal conductivity (κ), for thermoelectric and thermal barrier applications, and requires the study of highly pure materials. We synthesized the n-type sulfide CuPbBi5S9 with an ultralow κ value of 0.6-0.4 W m-1 K-1 in the temperature range 300-700 K. In contrast to prior studies, we show that this synthetic sulfide does not exhibit the ordered gladite mineral structure but instead forms a copper-deficient disordered aikinite structure with partial Pb replacement by Bi, according to the chemical formula Cu1/3□2/3Pb1/3Bi5/3S3. By combining experiments and lattice dynamics calculations, we elucidated that the ultralow κ value of this compound is due to very low energy optical modes associated with Pb and Bi ions and, to a smaller extent, Cu. This vibrational complexity at low energy hints at substantial anharmonic effects that contribute to enhance phonon scattering. Importantly, we show that this aikinite-type sulfide, despite being a poor semiconductor, is a potential matrix for designing novel, efficient n-type thermoelectric compounds with ultralow κ values. A drastic improvement in the carrier concentration and thermoelectric figure of merit have been obtained upon Cl for S and Bi for Pb substitution. The Cu1-x□xPb1-xBi1+xS3 series provides a new, interesting structural prototype for engineering n-type thermoelectric sulfides by controlling disorder and optimizing doping.