Key Inclusion Criteria/Common Criteria (Group 1 - Newly diagnosed glioblastoma, Group 2 - Recurrent glioblastoma):
1. Signed informed consent must be obtained prior to participation in the study
2. Age \>= 18 years
3. Histologically confirmed glioblastoma according to WHO classification established following either a surgical resection or biopsy
4. Participants who are receiving corticosteroid treatment with dexamethasone, must be treated with a dose of =\<4 mg/day (or other corticosteroids at equivalent dose) for a minimum of 7 days before initiation of study treatment
5. Adequate bone marrow and organ function as defined by the following laboratory values obtained prior to receiving the first study treatment:
1. Absolute Neutrophil Count (ANC) \>= 1.5 x 10\^9/L
2. Platelet count \>= 100 x 10\^9/L
3. Hemoglobin \>= 10.0 g/dL
4. Creatinine clearance \>= 60 mL/min calculated by the CKD-EPI (Chronic Kidney Disease Epidemiology Collaboration) creatinine equation .
5. Aspartate transaminase (AST) or Alanine transaminase (ALT) =\< 3.0 x ULN
6. Total bilirubin (TBIL) \< 1.5 × ULN (any elevated bilirubin should be asymptomatic at enrollment) except for participants with Gilbert's syndrome who may only be included if the total bilirubin is =\< 3.0 × ULN or direct bilirubin =\< 1.5 × ULN
7. Serum lipase ≤ 1.5 x ULN. For serum lipase \> ULN - =\< 1.5 x ULN, value must be considered not clinically significant and not associated with risk factors for acute pancreatitis
Key Inclusion Criteria/Newly diagnosed glioblastoma (Group 1):
9\. Availability of tumor tissue representative of glioblastoma from definitive surgery or biopsy, to support biomarker analysis 10. Presence of gadolinium enhancement at the tumor region in the pre-surgery MRI
Key Inclusion Criteria/Recurrent glioblastoma (Group 2) 11. Presence of \[68Ga\]Ga-NeoB uptake by PET/CT or PET/MRI at the tumor region 12. Having first or second glioblastoma recurrence, after standard therapy that includes prior radiation therapy (RT) and at least 12 weeks from completion of RT 13. Evidence of recurrent disease (RD) demonstrated by disease progression using modified Response Assessment in Neuro-Oncology (mRANO) criteria. RD must be documented with at least one bi-dimensionally measurable contrast-enhancing lesion with clearly defined margins by MRI scan, with minimal diameters of 10 mm, according to mRANO criteria. For those participants who will undergo a second surgery for recurrence, pre-surgery MRI will be used for confirmation of RD.
14\. If a second surgery is performed for glioblastoma recurrence, the following criteria must be met:
1. residual and measurable disease post-surgery is not required but surgery must have confirmed the recurrence diagnosis by MRI.
2. surgery completed at least 2 weeks prior to study treatment initiation, with post-surgery recovery without any complications related to surgical procedure.
Key Exclusion Criteria/Common Criteria (Group 1 - Newly diagnosed glioblastoma, Group 2 - Recurrent glioblastoma):
1\. Additional, concurrent, or active therapy for glioblastoma outside of the present study 4. History or current diagnosis of impaired cardiac function, clinically significant cardiac disease, or ECG abnormalities indicating significant risk of safety for study participants such as:
a. Documented myocardial infarction (MI), angina pectoris, cardiomyopathy, symptomatic pericarditis, or coronary artery bypass graft (CABG) within 6 months prior to study entry b. Long QT syndrome or family history of idiopathic sudden death or congenital long QT syndrome, or any of the following: i. Risk factors for Torsade de Pointes (TdP) including uncorrected hypocalcemia, hypokalemia or hypomagnesemia, history of cardiac failure, or history of clinically significant/symptomatic bradycardia ii. Concomitant medication(s) with a known risk to prolong the QT interval and/or known to cause Torsade de Pointes that cannot be discontinued or replaced by safe alternative medication (e.g., within 5 half-lives or 7 days prior to starting study drug) iii. Inability to determine the Fridericia QT correction formula (QTcF) interval c. Clinically significant cardiac arrhythmias (e.g., ventricular tachycardia), complete left bundle branch block, high-grade AV block (e.g., bifascicular block, Mobitz type II and third-degree AV block) d. Resting QTcF \>= 450 msec (male) or \>= 460 msec (female) e. Left Ventricular Ejection Fraction (LVEF) \<50% as determined by echocardiogram (ECHO) or Multiple Gated Acquisition (MUGA) scan f. Uncontrolled hypertension defined by a Systolic Blood Pressure (SBP) \>=160 mmHg and/or Diastolic Blood Pressure (DBP) \>=100 mm Hg, with or without anti-hypertensive medication.
5\. History of another active malignancy in the previous 3 years prior to study entry, except participants with prior history of superficial bladder cancer, any in situ carcinoma or basal or squamous cell skin cancer treated curatively
Key Exclusion Criteria/Newly diagnosed glioblastoma (Group 1):
17\. Any prior treatment for glioma of any grade, including: prolifeprospan 20 with carmustine wafer, intracerebral agent, radiation treatment, chemotherapy or immunotherapy
Key Exclusion Criteria/Recurrent glioblastoma (Group 2) 18. Previous treatment with bevacizumab for the treatment of glioblastoma with therapeutic intent, or with bevacizumab as supportive therapy (e.g., edema reduction) within 60 days of initiation of study treatment 19. More than two prior lines of systemic therapy, more than one surgical resection for recurrent disease and treatment with an intracerebral/intracranial agent prior to starting \[177Lu\]Lu-NeoB. Administration in adjuvant setting counts as a line of prior systemic treatment.
