Language processing has been suggested to be partially automatic, with some studies suggesting full automaticity and attention independence of at least early neural stages of language comprehension, in particular, lexical access. Existing neurophysiological evidence has demonstrated early lexically specific brain responses (enhanced activation for real words) to orthographic stimuli presented parafoveally even under the condition of withdrawn attention. These studies, however, did not control participants' eye movements leaving a possibility that they may have foveated the stimuli, leading to overt processing. To address this caveat, we recorded eye movements to words, pseudowords, and non-words presented parafoveally for a short duration while participants performed a dual non-linguistic feature detection task (color combination) foveally, in the focus of their visual attention. Our results revealed very few saccades to the orthographic stimuli or even to their previous locations. However, analysis of post-experimental recall and recognition performance showed above-chance memory performance for the linguistic stimuli. These results suggest that partial lexical access may indeed take place in the presence of an unrelated demanding task and in the absence of overt attention to the linguistic stimuli. As such, our data further inform automatic and largely attention-independent theories of lexical access.