Inclusion Criteria: * APOE4 homozygotes * Willing and able to provide informed consent (or consent provided by a legally authorized representative) * Clinical diagnosis of mild cognitive impairment due to Alzheimer's disease or mild to moderate dementia due to Alzheimer's disease * Evidence of CSF biomarkers consistent with Alzheimer's disease * Serum neutralizing anti-AAVrh10 titer \<1:100 * No evidence of active infection of any type, including hepatitis virus (A, B, or C) or human immunodeficiency virus (HIV-1 and HIV-2) * Fertile or infertile individuals; it will be recommended that fertile individuals utilize barrier birth control measures to prevent pregnancy for the duration of the study * Individuals not receiving experimental medications or participating in another experimental protocol for at least 4 weeks prior to entry into the study * Participants who agree not to post their personal data related to the study on social media. Exclusion Criteria: * Individuals receiving systemic immunosuppressant or corticosteroid therapy other than protocol-specified, are receiving a monoclonal anti-amyloid therapy (example, Aduhelm™ (aducanumab), Leqembi™ (lecanemab-irmb) or unable to wash out from anti-coagulant medications. * Individuals who do not fit the American Journal of Neuroradiology recommendations for image-guided spinal procedures * Presence of other significant medical, psychiatric, or neurological conditions may disqualify the participant from participation in this study, particularly those which would create an unacceptable risk of receiving the LX1001-01 vector, for example, malignancy, heart failure, liver or renal failure, or HIV positive. * Elevated white blood cell count, temperature \>38.5° C, infiltrate on chest x-ray. Note: Repeat of these examinations during the screening period is permitted to confirm eligibility * Prior or concurrent participation in any gene and/or cell therapy * Any condition, disorder, or abnormal laboratory test findings at screening which, in the judgment of the investigator, would interfere with the individual's ability to comply with all study requirements or would require the administration of treatment during the study that could potentially affect the interpretation of the study data, or would place the individual at unacceptable risk by his/her participation in the study * Individuals who cannot participate in magnetic resonance imaging, amyloid and tau PET scans, and CSF studies * Individuals who cannot undergo study-related procedures without general anesthesia (other than who need general anesthesia for the gene therapy administration) * More than 4 cerebral microhemorrhages (regardless of their anatomical location or diagnostic characterization as "possible" or "definite"), a single area of superficial siderosis, or evidence of a prior macro hemorrhage on screening MRI * Individuals with a history of clinically significant hypersensitivity or contraindication as judged by the investigator, to any component of the study drug formulation or to any drugs used in this study (examples are corticosteroids and proton-pump inhibitors) * Are pregnant or nursing