Comparing the Radiopharmaceutical Drug, [177Lu]Lu-DOTATATE, to Standard of Care Treatment for Patients With Meningioma That Has Come Back After Prior Treatment

Inclusion Criteria: STEP 1 REGISTRATION * Aged \>= 18 years * Histologically confirmed diagnosis of WHO grade 1-3 meningioma * Presence of measurable contrast-enhancing disease on gadolinium-enhanced MRI brain scan defined as at least one lesion with two perpendicular diameters measuring ≥10 mm on two or more axial slices (≤ 5 mm interslice thickness, ≤ 1 mm interslice gap) per current RANO meningioma criteria * Progression of disease determined by local radiology review per current RANO meningioma criteria, defined as * ≥ 15% increase in sum of product of perpendicular measurements of up to 5 measurable target lesions within the last 6 months, or * ≥ 25% increase in sum of product of perpendicular measurements of up to 5 measurable target lesions within the last 12 months, or * Development of a new measurable lesion * The following scans must be available for submission for central radiology review: * Pre-progression gadolinium-enhanced MRI brain scan * Progression gadolinium-enhanced MRI brain scan STEP 2 REGISTRATION * Progression of disease determined by central radiology review per current RANO meningioma criteria, defined as * ≥ 15% increase in sum of product of perpendicular measurements of up to 5 measurable target lesions within the last 6 months, or * ≥ 25% increase in sum of product of perpendicular measurements of up to 5 measurable target lesions within the last 12 months, or * Development of a new measurable lesion. * \[68Ga\]Ga-DOTATATE uptake on PET-CT. Positive uptake is defined as uptake at least as high as liver, based on the uptake in at least one target lesion. * If randomized to the control (standard of care) arm, both the patient and investigator must agree NOT to receive SSTR2-targeted therapy, surgical resection, or radiation therapy. * Patients must be willing and able to undergo regular MRI scans of the brain and \[68Ga\]Ga-DOTATATE PET-CT imaging during the study. * Patients must have recovered to CTCAE grade ≤1 or pretreatment baseline from clinically significant adverse events related to prior therapy (exclusions include alopecia, lymphopenia, sensory neuropathy ≤ grade 2, or other ≤ grade 2 not constituting a safety risk based on the investigator's judgment). * Adequate organ and bone marrow function as defined below (within 28 days prior to step 2 registration): * Absolute neutrophil count (ANC) ≥ 1500/mm3 * Platelet count ≥ 75,000/mm3 * Hemoglobin ≥ 8 g/dL * Creatinine clearance (calculated by the Cockroft-Gault method) ≥40mL/min * Total serum bilirubin ≤ 3 x ULN (except participants with Gilbert's Syndrome, who can have a total bilirubin ≤ 5 x ULN) * Potassium within normal limits. Exclusion Criteria: * Patients with a clinical diagnosis of NF2-related schwannomatosis or with a known molecular diagnosis of NF2-related schwannomatosis. * Patients with radiation-associated meningiomas. * Patients with known intraspinal meningiomas or meningioma metastases outside the skull/spinal column. * Prior SSTR2-targeted therapy, e.g. Somatostatin LAR or short-acting Octreotide. * Unstable neurological symptoms requiring steroids to control symptoms at a dose of \>2 mg of dexamethasone (or equivalent) daily within 28 days prior to step 2 registration. * Patients requiring immediate local therapy (e.g. surgical resection). * Surgical procedure within the timeframes listed below, prior to step 2 registration. * 28 days from any prior craniotomy * 7 days from stereotactic biopsy Note: There is no limit to the number of prior surgical interventions * Treatment within the timeframes specified below, prior to step 2 registration. * 28 days (or 5 half-lives, whichever is longer) for cytotoxic chemotherapy, biologic agent, investigational agent or any other systemic agent prescribed for the purpose of treating meningioma * 6 weeks from nitrosoureas Note: There is no limit to the number of prior systemically administered therapeutic agents. * Prior external beam radiation, interstitial brachytherapy or stereotactic radiosurgery cumulative radiation dose of \> 70 Gy or the last dose of radiotherapy \< 24 weeks (6 months) prior to step 2 registration * Peptide receptor radionuclide therapy at any time prior to registration. * Known hypersensitivity to somatostatin analogues or any component of the \[68Ga\]Ga- DOTATATE or \[177Lu\]Lu-DOTATATE formulations. * Active infection requiring current use of intravenous therapy with antibiotics. * Active cardiovascular disease: cerebral vascular accident/stroke (≤ 6 months prior to registration), myocardial infarction (≤ 6 months prior to registration), congestive heart failure (≥ NYHA class II), unstable angina pectoris, or serious cardiac arrhythmia requiring medication. * An active malignancy ≤ 3 years. Note: Patients with a malignancy whose natural history or treatment does not have the potential to interfere with the safety or efficacy assessment of the investigational regimen are eligible for this trial. * Pregnant and/or breastfeeding patients who are unwilling to discontinue breast feeding. * Participants of childbearing potential must have a negative pregnancy test within 14 days of study entry.