Inclusion Criteria:

* 1. Age ≥12 years and weight \>40 kg;

2. Histologically confirmed diagnosis per 2016 World Health Organization (WHO) classification of lymphoid neoplasms160 and per the 2016 WHO classification of acute leukemia161 of the following indications:

• DLBCL, including arising from follicular lymphoma;

• High-grade B-cell lymphoma;
* MCL;
* Primary mediastinal large B-cell lymphoma;
* Primary DLBCL of the CNS;
* Burkitt or Burkitt-like lymphoma/leukemia;
* CLL/SLL; or
* B-lymphoblastic leukemia/lymphoma, T-lymphoblastic leukemia/lymphoma, acute leukemia/lymphoma, acute leukemias of ambiguous lineage, or NK cell lymphoblastic leukemia/lymphoma;

3. Patients must have R/R disease with prior therapies defined below:
* DLBCL and high-grade B-cell lymphoma:

1. R/R after autologous HCT; or
2. R/R after CAR T therapy; or
3. Ineligible for autologous HCT or CAR T therapy due to persistent disease, co-morbidity, or social issues (eg, lack of insurance, lack of caregiver, etc); or
4. R/R after ≥2 lines of therapy including anti-20 antibody. Patients must have failed or are intolerant or ineligible for polatuzamab vedotin;
* MCL:

1. R/R after autologous HCT; or
2. Ineligible for autologous HCT due to persistent disease, co-morbidity, or social issues (eg, lack of insurance, lack of caregiver, etc); or
3. R/R after ≥2 lines of therapy including at least 1 of the following: a BTK inhibitor, bortezomib, or lenalidomide;
* Primary mediastinal large B-cell lymphoma:

a. R/R after ≥1 line of therapy; AVM Biotechnology, LLC. Clinical Study Protocol AVM0703-001 Confidential \& Proprietary Page 47 of 105 Version 1.0, 20 February 2020
* Primary DLBCL of the CNS:

a. R/R after ≥1 line of therapy including methotrexate (unless intolerant to methotrexate);
* Burkitt or Burkitt-like lymphoma/leukemia:

1. R/R after autologous or allogeneic HCT; or
2. Ineligible for autologous or allogeneic HCT due to persistent disease, co-morbidity, or social issues (eg, lack of insurance, lack of caregiver, etc);
* CLL/SLL:

1. R/R after autologous or allogeneic HCT; or
2. Ineligible for autologous or allogeneic HCT due to persistent disease, co-morbidity, or social issues (eg, lack of insurance, lack of caregiver, etc); or
3. R/R after ≥2 lines of therapy including at least 1 of the following: a BTK inhibitor, ventoclax, idelalisib, or duvelisib;
* ALL:

1. R/R after autologous or allogeneic HCT; or
2. Ineligible for allogeneic HCT due to persistent disease, co-morbidity, or social issues (eg, lack of insurance, lack of caregiver, etc); or
3. R/R according to the following disease-specific specifications:
* B-cell lymphoblastic leukemia/lymphoma: ≥2 lines of therapy including approved CAR T cell therapies, inotuzumab, ozogamicin, or blinatumomab; or
* T-cell lymphoblastic leukemia/lymphoma: Patients must have failed nelarabine; or
* NK cell lymphoblastic leukemia/lymphoma: R/R after ≥1 line of therapy;

4. Lansky (12 to 15 years of age) (Appendix G) or Karnofsky (≥16 years of age) (Appendix H) performance status ≥50;

5. Screening laboratory values that meet all of the following criteria:
* Absolute neutrophil count ≥0.5 × 109/L;
* Platelet count \>50 × 109/L;
* Hemoglobin ≥8.0 g/dL;
* Aspartate aminotransferase or alanine aminotransferase ≤2.5 × ULN, unless due to the disease;
* Total bilirubin ≤1.5 × ULN (if secondary to Gilbert's syndrome, ≤3 × ULN is permitted), unless due to the disease; and
* Serum creatinine ≤1.5 × ULN or glomerular filtration rate ≥50 mL/min (calculated from a 24-hour urine collection);

6. Minimum level of pulmonary reserve defined as \
7. Females of childbearing potential must have a negative serum pregnancy test at screening. Females of childbearing potential and nonsterile males must agree to use medically effective methods of contraception from the time of informed consent/assent through 1 month after study drug infusion, which must, at a minimum, include a barrier method; and

8. The ability to understand and willingness to sign a written informed consent form (ICF) and the ability to adhere to the study schedule and prohibitions. Patients under the age of 18 years (or other age as defined by regional law or regulation) must be willing and able to provide written assent and have a parent(s) or guardian(s) willing and able to provide written, signed informed consent after the nature of the study has been explained and prior to performance of any study-related procedure.

Exclusion Criteria:

* Patients who meet any of the following criteria will be excluded from participation in the study:

1. History of another malignancy, except for the following:

* Adequately treated local basal cell or squamous cell carcinoma of the skin;
* Adequately treated carcinoma in situ without evidence of disease;
* Adequately treated papillary, noninvasive bladder cancer; or
* Other cancer that has been in complete remission for ≥2 years. Patients with low-grade prostate cancer, on active surveillance, and not expected to clinically progress over 2 years are allowed;
2. Significant cardiovascular disease (eg, myocardial infarction, arterial thromboembolism, cerebrovascular thromboembolism) within 3 months prior to the start of AVM0703 administration, angina requiring therapy, symptomatic peripheral vascular disease, New York Heart Association Class III or IV congestive heart failure, left ventricular ejection fraction \<30%, left ventricular fractional shortening \<20%, or uncontrolled ≥Grade 3 hypertension (diastolic blood pressure \[DBP\] ≥100 mmHg or systolic blood pressure \[SBP\] ≥150 mmHg) despite antihypertensive therapy for patients ≥18 years of age, or uncontrolled stage 2 hypertension (DBP ≥90 mmHg or SBP ≥140 mmHg) despite antihypertensive therapy for patients ≥12 years of age;
3. Significant screening electrocardiogram (ECG) abnormalities, including unstable cardiac arrhythmia requiring medication, atrial fibrillation/flutter, left bundle-branch block, second-degree atrioventricular (AV) block type 2, third-degree AV block, ≥Grade 2 bradycardia, or heart rate corrected QT interval using Fridericia's formula average of triplicate ECGs \>450 msec;
4. Known gastric or duodenal ulcer;
5. Uncontrolled type 1 or type 2 diabetes;
6. Known hypersensitivity or allergy to the study drug or any of its excipients;
7. Untreated ongoing bacterial, fungal, or viral infection (including upper respiratory tract infections) at the start of AVM0703 administration, including the following:

* Positive hepatitis B surface antigen and/or hepatitis B core antibody test plus a positive hepatitis B polymerase chain reaction (PCR) assay. Patients with a negative PCR assay are permitted with appropriate antiviral prophylaxis;
* Positive hepatitis C virus antibody (HCV Ab) test. Patients with a positive HCV Ab test are eligible if they are negative for hepatitis C virus by PCR;
* Positive human immunodeficiency virus (HIV) antibody test with detectable HIV load by PCR, or the patient is not able to tolerate antiretroviral therapy; or
* Positive testing for tuberculosis during screening;
8. Received live vaccination within 8 weeks of screening;
9. Pregnant or breastfeeding;
10. Concurrent participation in another therapeutic clinical study; or
11. Manic-depressive disorder, schizophrenia, or a history of severe depression or substance abuse.