Amyotrophic lateral sclerosis (ALS) is biologically heterogeneous, and oxidative injury can contribute to degeneration while also reflecting downstream damage or adaptive responses. Glutathione S-transferase Pi 1 (GSTP1) combines glutathione-dependent detoxification with non-canonical regulation of c-Jun N-terminal kinase (JNK), but the biochemical evidence for direct GSTP1–JNK coupling largely comes from non-ALS systems. This narrative review separates human ALS observations, functional ALS-model findings, and extrapolated mechanisms. Altered GSTP1 abundance or total GST activity in ALS does not establish GSTP1-specific impairment or causality. JNK-related injury has stronger functional support in selected ALS models involving DLK/MAP3K12, ASK1, HIPK2, and MAP4K4. Ferroptosis-related findings are concentrated in SOD1 models, with additional evidence of susceptibility in FUS cellular models, and do not establish a GSTP1–JNK–ferroptosis cascade. We distinguish neuronal and glial context and the execution of apoptosis versus ferroptosis. Decisive tests combine GSTP1 perturbation with catalytic and interaction-deficient rescue, direct binding and JNK-activity assays, and pathway-specific cell-death rescue. GSTP1 remains a candidate context-dependent modifier of shared neurodegenerative processes; causal validation, reproducible pathway biomarkers, and safety assessment are required before therapeutic translation.