This will be a follow-up study to the Comparison of High Dose vs. Standard Dose Influenza Vaccine in Lung Allograft Recipient study (DMID Protocol Number 22-0014) at Vanderbilt University Medical Center. Lung transplantation is a life-saving therapy for patients with advanced lung disease, and is also associated with an improvement in quality of life. However, due to the need for life-long immunosuppression to prevent acute cellular rejection and chronic lung allograft dysfunction (chronic rejection), lung transplant recipients are at risk for developing major infections. In fact, one-year survival is 85%, with infection being the leading cause of death within the first year post-transplant. We will conduct a follow-up phase II, randomized, double-blind trial to assess the impact of subsequent administration of two doses of HD-IIV compared to two doses of SD-IIV among lung recipients during the early post-transplant period. Demonstration of improved immunogenicity from two doses of HD-IIV over consecutive influenza seasons would provide potential broad benefit in reducing influenza disease and its associated complications in lung transplant recipients. Moreover, studying vaccine immunogenicity and safety in the same participants over consecutive years can provide insight into the influence of immunosuppression levels and allograft aging on vaccine-mediated immune modulation. This proposed study design will contribute significantly to influenza vaccination guidance and policy for the highly vulnerable lung transplant population. This proposed study is designed to address several key knowledge gaps in vaccine-mediated protection of lung transplant recipients against influenza: * Is there increased immunogenicity with administration of one or two doses of HD-IIV or SD-IIV in the subsequent season compared to two doses of HD-IIV or SD-IIV in the first season? * What is the durability of the humoral and cellular immune response between influenza seasons and does two doses of HD-IIV or SD-IIV sustain higher HAI titers compared to two doses of HD-IIV or SD-IIV in the first season? * What is the impact of maintenance immunosuppression levels on influenza vaccine immunogenicity within the same participant? * Will the optimal immunogenic vaccination strategy be associated with an acceptable long-term safety profile over successive influenza seasons, including injection-site and systemic reactions, allosensitization, and organ rejection?