Inclusion Criteria:
For all participants
Criteria to be met prior to enrolment in the trial:
* Aged 16 years or over.
* Written (signed and dated) informed consent and be capable of co-operating with ALETA-001 administration and follow-up.
* Confirmed diagnosis of B-cell NHL according to World Health Organization (WHO) 2016 criteria.
* Eastern Cooperative Oncology Group performance status of 0, 1 or 2.
* Biochemical indices within protocol specified ranges.
Cohort Specific Inclusion criteria (for Phase I Cohorts A \& B) Criteria to be met prior to enrolment in the trial.
* Histologically confirmed diagnosis of relapsed/refractory LBCL or MCL.
* Have received an approved anti-CD19 CAR T-cell therapy.
* Objectively evaluable or measurable disease at 4 weeks (±1 week) post CAR T, which demonstrates:
* inadequate or incomplete response (PR or SD), or
* PD if there is a reasonable expectation of deriving benefit from trial treatment, or
* initial response followed by relapse within 9 months assessed according to Lugano Criteria.
* Haematological indices within protocol specified ranges.
Cohort Specific Inclusion criteria (for Phase I Cohorts C \& D) Criteria to be met prior to lymphodepleting chemotherapy for CAR T therapy.
* Histologically confirmed diagnosis of relapsed/refractory LBCL or MCL.
* Approved by the UK national CAR T Clinical Panel (NCCP) to receive an approved anti-CD19 CAR T-cell therapy.
* Haematological indices within protocol specified ranges.
* Adequate cardiac function within protocol specified ranges with no clinical symptoms or signs of heart failure.
* Resting O2 saturation of ≥92% on room air.
Eligibility for participants in Phase II of the trial will depend on timing of administration of ALETA-001 which will be recommended by the Safety Review Committee (SRC).
Exclusion Criteria for all participants:
* Active or previous malignancies of other types that, in the opinion of the Investigator, should exclude the participant. Exceptions include adequately treated cone biopsied in situ carcinoma of the cervix uteri and basal or squamous cell carcinoma of the skin and patients with asymptomatic prostate cancer without known metastatic disease and with no requirement for therapy or who require only hormonal therapy and have had normal prostate specific antigen for \>1 year prior to the start of therapy. Cancer survivors, who have undergone potentially curative therapy for a prior malignancy, have no evidence of that disease for 2 years or more and are deemed at negligible risk for recurrence, are eligible for the trial.
* Any ongoing toxic manifestation of previous anti-cancer treatment that, in the opinion of the Investigator, should exclude the participant.
* Ongoing need for systemic immunosuppressive therapy other than replacement dose of corticosteroids. Intermittent topical, inhaled or intranasal corticosteroids are permitted.
* Presence of active infections and/ or inflammatory disease requiring active management.
* Documented current central nervous system involvement by lymphoma.
* Women of childbearing potential (or are already pregnant or lactating) unless willing to adhere to protocol-defined contraceptive requirements.
* Male patients with partners of childbearing potential unless willing to adhere to protocol-defined contraceptive requirements.
* Major thoracic or abdominal surgery from which the participant has not yet recovered.
* At high medical risk because of non-malignant systemic disease including active uncontrolled infection.
* Hypersensitivity to any of the ingredients/excipients in ALETA-001.
* Participation in another interventional clinical trial, whilst taking part in this trial of ALETA-001. Participation in an observational trial or interventional clinical trial that does not involve administration of an IMP and that would not place an unacceptable burden on the participant, in the opinion of the Investigator and CDD, would be acceptable.
* Participants with any congenital or acquired immunodeficiency syndrome or who are receiving immunosuppressive therapy (including any dose of systemic corticosteroids), or who are immunosuppressed post organ transplant. However, participants receiving inhaled corticosteroids and participants with a history of allergy (other than anaphylaxis) are eligible, as are participants with a history of autoimmune disease.
* Any other condition that, in the Investigator's opinion, would mean that the trial is not in the best interests of the participant.
* Concurrent radiotherapy (except for palliative reasons).
Cohort specific exclusion criteria prior to enrolment in the trial (for Phase I
Cohorts A \& B):
* Participants who have received any other systemic anti-cancer treatment post-CAR T.
* Potential participants who experienced any of the following because of the initial CAR T treatment:
* Grade 4 CRS or ICANS post CAR T infusion.
* Grade ≥3 CRS or ICANS persisting beyond 7 days despite optimal therapy.
* Any Grade ≥1 CRS or ICANS must have fully resolved.
* Any Grade ≥3 organ toxicity (other than haematologic toxicity) following CAR T infusion must have improved to Grade ≤2 for at least 48 hours prior to ALETA-001 infusion.
Cohort specific exclusion criteria prior to ALETA-001 infusion between Day 10-18 post CAR T-cell infusion (for Phase I Cohorts C \& D):
* Grade 4 CRS or ICANS post CAR T infusion.
* Grade ≥3 CRS or ICANS persisting beyond 7 days despite optimal therapy.
* Any Grade ≥2 CRS or ICANS must have improved to Grade ≤1 for at least 48 hours prior to ALETA-001 infusion.
* ECOG performance status ≥3.
* Any Grade ≥3 organ toxicity (other than haematologic toxicity) following CAR T infusion must have improved to Grade ≤2 for at least 48 hours prior to ALETA-001 infusion.
* Any unresolved serious active infection which in the opinion of the Investigator precludes ALETA-001 infusion (ongoing need for IV antimicrobial therapy per se is not an exclusion).
