This study is researching an experimental drug called odronextamab (referred to as study drug), in combination with lenalidomide. The study is focused on participants who have one of two types of cancer: follicular lymphoma (FL) or marginal zone lymphoma (MZL) that has come back after treatment (called relapsed), or did not respond to treatment (called refractory). FL and MZL are subtypes of Non-Hodgkin 's lymphoma (NHL). This study will be made up of two parts (Part 1 not randomized, Part 2 randomized - controlled). The aim of Part 1 of the study is to see how safe and tolerable the study drug is when used in combination with lenalidomide, in participants with FL or MZL, and to determine the dose of the study drug to be used in Part 2 of this study. This combination is considered first-in-human as it has not been tested as a combination treatment in humans before. The aim of Part 2, of the study is to assess how the combination of the study drug and lenalidomide works compared to the combination of rituximab (called the comparator drug) and lenalidomide. The combination of comparator drug and lenalidomide is the current standard-of care treatment for FL and/or MZL. Standard of care means the usual medication expected and used when receiving treatment for a condition. The study is looking at several other research questions, including: * What side effects may happen from taking the study drug in combination with lenalidomide * How much study drug is in the blood at different times * Whether the body makes antibodies against the study drug (which could make the study drug less effective or could lead to side effects) * The impact from the study drug on quality of life and ability to complete routine daily activities