Inclusion Criteria:  Participants must have a clinical diagnosis of Lynch syndrome (LS) as defined by:  Mutation-positive LS: carriers or obligate carriers (by pedigree) of a pathogenic germline mutation or likely pathogenic mutation in mismatch repair (MMR) genes (MLH1, MSH2/EPCAM, MSH6, or PMS2) Mutation-negative LS (also known as "Lynch-like syndrome" or "suspected Lynch syndrome): individuals with a personal history of a non-sporadic MMR-deficient premalignant lesion (i.e., colorectal polyp) or a non-sporadic MMR-deficient malignant tumor (where "non-sporadic MMR deficient" is defined by either immunohistochemistry with loss of MLH1, MSH2, MSH6, or PMS2 expression or microsatellite instability (MSI) testing by polymerase chain reaction (PCR) or both, but no evidence of MLH1 promoter methylation in cases with loss of both MLH1 and PMS2, and/or no evidence of BRAF mutation in cases with loss of both MLH1 and PMS2) but germline MMR genetic testing showing either a variant of unknown significance, or mutation negative result, or had declined germline MMR genetic testing Participants must have no evidence of active or recurrent invasive cancer for 6 months prior to screening and must be at least 6 months from any prior cancer-directed treatment (such as surgical resection, chemotherapy, immunotherapy, hormonal therapy, or radiation) Participants must have endoscopically accessible distal colon and/or rectal mucosa (i.e., participants must have at least part of the descending/sigmoid colon and/or rectum intact) Participants must consent to standard of care surveillance with colonoscopy with biopsies every 12 months Participants must consent to refrain from using aspirin or non-steroidal anti-inflammatory drugs (NSAIDs) or cyclooxygenase (COX) inhibitors for the duration of the trial, except for cardio-preventive aspirin (< 100 mg daily). Individuals taking such drugs may not be enrolled unless they are willing to stop the medications (and possibly change to alternative non-excluded medications to treat the same conditions) no less than 1 month prior to enrollment. Participants will discuss with their primary care provider/local provider about the discontinuation of such medication(s) and obtain approval prior to stopping any agent Age >= 18 years. Because no dosing or adverse event (AE) data are currently available on the use of Nous-209 in participants < 18 years of age, children are excluded from this study but will be eligible for future pediatric trials, if applicable Eastern Cooperative Oncology Group (ECOG) performance status =< 1 (Karnofsky >= 70%) Hemoglobin >= 10 g/dL or hematocrit >= 30 % Leukocyte count >= 3,500/microliter Platelet count >= 100,000/microliter Absolute neutrophil count >= 1,500/microliter Creatinine clearance (calculated if measured is not available) >= 60 mL/min/1.73 m^2 Aspartate aminotransferase (AST) (serum glutamic oxaloacetic transaminase [SGOT])/alanine aminotransferase (ALT) (serum glutamic pyruvic transaminase [SGPT]) =< 2 times the institutional upper limit of normal (ULN) Total bilirubin =< 1.5 the ULN; participants with Gilbert's disease may be enrolled with higher total bilirubin if their direct bilirubin is =< 1.5 times the ULN Participants must consent to refrain to receive any other type of vaccination during the first 10 weeks of the trial Participants must consent to refrain from receiving adenoviral-based vaccines for the duration of the trial (including the period from week 9 to week 52) Willing and able to adhere to the prohibitions and restrictions specified in the final approved protocol The effects of Nous-209 on the developing human fetus at the recommended therapeutic dose are unknown. For this reason, women of child-bearing potential and men must agree to use adequate contraception (hormonal or barrier method of birth control; abstinence) prior to study entry for the duration of study participation (12 months) and 6 months after end of study. Should a woman become pregnant or suspect she is pregnant while participating in this study, she should inform her study physician immediately Ability to understand and the willingness to sign a written informed consent document (available for both English- and Spanish-speaking individuals)  Exclusion Criteria:  Prior receipt of a recombinant adenoviral or MVA vaccine including COVID19 adenovirus vaccines within the previous 6 months Histologically-confirmed high-grade dysplasia or cancer on biopsy at screening Individuals with active malignancy (excluding non-melanoma skin cancer) Any serious uncontrolled and/or unstable pre-existing medical disorder (aside from malignancy exception above), psychiatric disorder, or other conditions that could interfere with participant's safety, obtaining informed consent, or compliance to the study procedures Active infection (acute and self-limited) or human immunodeficiency virus (HIV), hepatitis B virus (HBV), or hepatitis C virus (HCV) infection. Participants with laboratory evidence of cleared HBV and HCV infection will be permitted History of organ allograft or other history of immunodeficiency Known immediate or delayed hypersensitivity reaction or idiosyncrasy to drugs chemically related to study drug, or excipients, or to egg proteins Individuals with a condition requiring systemic treatment with either corticosteroids (> 10 mg daily prednisone equivalents) or other immunosuppressive medications (such as infliximab, rituximab, adalimumab, tacrolimus) within 14 days of study drug administration. Inhaled or topical steroids and adrenal replacement doses > 10 mg daily prednisone equivalents are permitted in the absence of active autoimmune disease Pregnant or breastfeeding or planning to become pregnant within 6 months after the end of study. Because there is an unknown but potential risk for adverse events (AEs) in nursing infants secondary to treatment of the mother with Nous-209, breastfeeding should be discontinued if the mother is treated with Nous-209 Men attempting or planning to conceive children during the study or within 6 months after the end of the study Participants may not be receiving any other investigational agents