Assessing effort in speech comprehension for hearing-impaired (HI) listeners is important, as effortful processing of speech can limit their hearing rehabilitation. We examined the measure of pupil dilation in its capacity to accommodate the heterogeneity that is present within clinical populations by studying lexical access in users with sensorineural hearing loss, who perceive speech via cochlear implants (CIs). We compared the pupillary responses of 15 experienced CI users and 14 age-matched normal-hearing (NH) controls during auditory lexical decision. A growth curve analysis was applied to compare the responses between the groups. NH listeners showed a coherent pattern of pupil dilation that reflects the task demands of the experimental manipulation and a homogenous time course of dilation. CI listeners showed more variability in the morphology of pupil dilation curves, potentially reflecting variable sources of effort across individuals. In follow-up analyses, we examined how speech perception, a task that relies on multiple stages of perceptual analyses, poses multiple sources of increased effort for HI listeners, wherefore we might not be measuring the same source of effort for HI as for NH listeners. We argue that interindividual variability among HI listeners can be clinically meaningful in attesting not only the magnitude but also the locus of increased effort. The understanding of individual variations in effort requires experimental paradigms that (a) differentiate the task demands during speech comprehension, (b) capture pupil dilation in its time course per individual listeners, and (c) investigate the range of individual variability present within clinical and NH populations.