Participating in critical reading in digital environments requires more than careful analysis of a single text. University EFL students are increasingly confronted with claims circulated throughout search results, news outlets, social media, institutional websites, and a multitude of interconnected resources. This theoretical paper establishes a framework for Epistemic-Lateral Reading (ELR) within the context of English as a Foreign Language (EFL) in tertiary education. A focused conceptual synthesis was conducted, integrating studies on Civic Online Reasoning and lateral reading, the RESOLV framework for task-driven reading, internet-specific epistemic validation, multi-document literacy, and EFL source evaluation. The synthesis indicates that the reliability of the source and the accuracy of the claim should be seen as interrelated but distinct assessments. It also suggests that EFL readers may conflate language accessibility, content relevance, or polished presentation with evidential reliability. ELR systematically organises digital critical reading into six coherent operations: articulating the thesis and purpose, scrutinising provenance, evaluating source reliability beyond the initial page, corroborating assertions through external sources, reconciling inconsistencies while modulating confidence, and constructing a judgment supported by sources in English. The framework is proposed as a theoretical model rather than an evidence-based strategy. It offers pedagogical applications and substantiated theories for subsequent exploration. ELR may enable a shift in EFL teaching from a checklist-based assessment of sources to an emphasis on evidence networks, provenance, corroboration, and justified uncertainty, while still providing language support for complex digital reading.