Predator-prey theory is commonly used to describe tumor growth in the presence of selective pressure from the adaptive immune system. These interactions are mediated by the tumor immunopeptidome (what the tumor "shows" the body) and the T-cell receptor (TCR) repertoire (how well the body "sees" cancer cells). The tumor immunopeptidome comprises neoantigens which can be gained and lost throughout tumorigenesis and treatment. Heterogeneity in the immunopeptidome is predictive of poor response to immunotherapy in some tumor types, suggesting that the TCR repertoire is unable to support a fully polyclonal response against every neoantigen. Importantly, while tumor and T-cell populations are known to compete with each other for intratumoral resources, whether between-lineage competition among peripheral T cells influences the TCR repertoire is unknown and difficult to interrogate experimentally. Computational models may offer a way to investigate these phenomena and deepen our understanding of the tumor-immune axis. Here, we construct a predator-prey-like model and calibrate it to preclinical and clinical data to describe tumor growth and immunopeptidome diversification. Simultaneously, we model the expansion of antigen-specific T-cell lineages and their consumption of both lineage-specific antigenic resources and lineage-agnostic, shared resources. This predator-prey-like framework accurately described clinically observed immunopeptidomes; recapitulated response-associated effects of immunotherapy, including immunoediting; and allowed exploration of treatment of tumors with varying growth and mutation rates.