<p>Language comprehension and production are predominantly supported by the left-lateralized <i>language-related network (LRN)</i>. However, right-hemispheric homologs of the language regions can also contribute to language processing, resulting in reduced left-hemispheric language lateralization. To date, it remains unclear whether less left-hemispheric language lateralization is associated with the recruitment of other non-language networks and their interaction with the <i>LRN</i> during language processing. In this study, we investigated how the degree of left-hemispheric language lateralization in healthy adults relates to the activation of non-language networks and the <i>LRN</i> connectivity to those networks. We applied independent component analysis to task-based functional magnetic resonance imaging data with sentence completion collected from 50 healthy adults. Instead of a single network, we identified the left-lateralized <i>LRN</i> and a mirror right-lateralized <i>LRN</i>. During language processing, the salience network was co-activated alongside the left-lateralized <i>LRN</i> and the right-lateralized <i>LRN</i>, regardless of individual language lateralization. We found that a weaker degree of lateralization was not associated with either domain-general network activation or left-lateralized <i>LRN</i> connectivity to domain-general networks. However, we present novel evidence that stronger right-hemispheric involvement in language processing is associated with greater left-lateralized <i>LRN</i> connectivity to the <i>cingulo-opercular network (CON)</i>. Given the role of the <i>CON</i> in the action mode, this result might indicate greater cognitive control to support language processing in people with stronger right-hemispheric involvement in language processing.</p>