The dose conformation and the sparing of neighboring critical healthy structures are improved in carbon-ion beam radiotherapy in comparison to conventional photon radiotherapy. Inter and intrafractional plan adaptation strategies may preclude the quality assurance (QA) of the actually applied treatment plan before the treatment starts. Therefore, independent measurements of the positions of scanned pencil C ion beams are of interest in order to monitor the beam application during the treatment and the beam in the isocenter. In this work, secondary ions outgoing from a patient-like phantom are exploited for the assessment of the lateral pencil beam position in a clinic-like C treatment fraction. The experiment was performed at the Heidelberg Ion-Beam Therapy Center (HIT) in Germany. A carbon-ion treatment plan was used to treat a 100 cm tumor volume in the center of an Alderson head phantom. Two silicon pixel detectors based on the Timepix3 technology developed at CERN were operated in synchronization to detect and to track outgoing secondary ions. We established an analysis of the measured secondary ion track distribution which enabled us to follow the beam scanning movement of the carbon-ion pencil beam by assessing the lateral position of the single beam spots. The precision of the developed method was found to range from 0.84 mm to 2.59 mm. For beam energies greater than 197.58 MeV/n, the mean of absolute distances of the measured lateral pencil beam positions with respect to the pencil beam positions measured by the beam application system (averaged over each energy layer) were smaller than 2 mm. We conclude that the presented method has shown capabilities of monitoring the lateral pencil beam positions by means of secondary ions with precision and sensitivity of clinical interest.