The construction of ferroptosis-related lncRNA prognostic models in malignancies has been an intense area of research recently. However, most of the studies focused on the exact expression of lncRNAs and had limited application values. Herein, we aim to establish a novel prognostic model for gastric cancer (GC) patients and discuss its correlation with immune landscapes and treatment responses. The present study retrieved transcriptional data of GC patients from the Cancer Genome Atlas (TCGA) database. We identified differentially expressed ferroptosis-related lncRNAs between tumor and normal controls of GC samples. Based on a new method of cyclically single pairing, we constructed a 0 or 1 matrix of ferroptosis-related lncRNA pairs (FRLPs). A risk score signature consisting of 10 FRLPs was established using multi-step Cox regression analysis. Next, we performed a series of systematic analyses to investigate the association of the FRLP model and tumor microenvironment, biological function, and treatment responses. An alternative model to the FRLP risk score signature, the gene set score (GS) model was also constructed, which could represent the former when lncRNA expression was not available. We established a novel prognostic signature of 10 ferroptosis-related lncRNA pairs. High-risk patients in our risk score model were characterized by high infiltration of immune cells, upregulated carcinogenic and stromal activities, and heightened sensitivity to a wide range of anti-tumor drugs, whereas low-risk patients were associated with better responses to methotrexate treatment and elevated immunotherapeutic sensitivity. The practicability of the FRLP risk score model was also validated in two independent microarray datasets downloaded from Gene Expression Omnibus (GEO) using the GS model. Finally, two online dynamic nomograms were built to enhance the clinical utility of the study. In this study, we developed a ferroptosis-related lncRNA pair-based risk score model that did not rely on the exact lncRNA expression level. This novel model might provide insights for the accurate prediction and comprehensive management for GC patients.