Inclusion Criteria:

        Part A - single-agent dose-escalation part:

        - Patients with histologically confirmed solid tumors or non-Hodgkin's lymphoma (NHL).

        J-arm of Part A - single-agent dose escalation in Japanese - Japanese patients with
        histologically confirmed solid tumors. Patients with tumors known to be positive for DDR
        (deoxyribonucleic acid damage repair) defects (such as ATM (ataxia-telangiectasia mutated)
        deleterious mutation or low ATM expression) can be included.

        Part A.1 - single-agent dose escalation part with alternative dosing schedule

        - Patients with histologically confirmed solid tumors or NHL known to be positive for ATM
        loss and/or ATM deleterious mutations will be included.

        Part B - single-agent expansion part:

          -  Patients with DDR deficiency biomarker-positive advanced solid tumors of the following
             histologies: i) CRPC (castration-resistant prostate cancer); ii) HER2-negative BC that
             is hormone-receptor positive (estrogen-receptor positive, progesterone-receptor
             positive, or both) or TNBC (triple negative BC); iii) CRC (colorectal cancer), and iv)
             gynecological tumors (ovarian, primary peritoneal, and fallopian tube cancers,
             endometrial cancer, or cervical cancer).

          -  The biomarker status of patients in Part B will be evaluated before general screening
             and only patients with the presence of the putative biomarkers of DDR deficiency will
             be recruited into general screening.

          -  Patients with histologically confirmed advanced cancer, regardless of the cancer type,
             or NHL and loss of ATM protein by IHC.

        The following inclusion criteria apply to ALL (dose-escalation and expansion) patients:

          -  Patients with tumors resistant or refractory to standard treatment and in which, in
             the opinion of the investigator, experimental treatment with BAY1895344 may be of
             benefit, Furthermore, no standard therapy would confer clinical benefit to the
             patient.

          -  Eastern Cooperative Oncology Group (ECOG) performance status of 0 to 1.

          -  Patients must have adequate bone marrow function as assessed by the following
             laboratory tests to be conducted within 7 (+2) days before the first dose of study
             drug. Note that the below values are to be independent of red blood cell transfusions
             or granulocytes colony-stimulating factor (G-CSF) (i.e., no red blood cell or
             platelets transfusion within 28 days prior to the screening complete blood count (CBC)
             result, or administration of G-CSF is to occur within 14 days prior to the CBC
             result):

               1. Hemoglobin ≥ 9 g/dL; patients with chronic erythropoietin treatment consistent
                  with institutional guidelines can be included.

               2. Absolute neutrophil count (ANC) ≥ 1.5X10^9/L (≥ 1500/mm^3)

               3. Platelet count ≥ 100X10^9/L (≥100,000/mm^3)

        Exclusion Criteria:

          -  Known hypersensitivity to the study drugs or excipients of the preparations or any
             agent given in association with this study

          -  History of cardiac disease: congestive heart failure New York Heart Association (NYHA)
             class >II, unstable angina (angina symptoms at rest), new-onset angina (within the
             past 6 months before study entry), myocardial infarction within the past 6 months
             before study entry, or cardiac arrhythmias requiring anti-arrhythmic therapy (beta
             blockers, calcium channel blockers, and digoxin are permitted)

          -  Moderate or severe hepatic impairment, i.e. Child-Pugh class B or C

          -  Patients with known human immunodeficiency virus (HIV) infection

          -  Patients who have an active hepatitis B virus (HBV) or hepatitis C virus (HCV)
             infection requiring treatment. Patients with chronic HBV or HCV infection are eligible
             at the investigator's discretion provided that the disease is stable and sufficiently
             controlled under treatment.

          -  Infections of CTCAE(Common Terminology Criteria for Adverse Events Version) Grade 2
             not responding to therapy or active clinically serious infections of CTCAE Grade >2