A Single Ascending Dose Study in Healthy Participants and Multiple Dose Study of JNJ-55920839 in Participants With Mild to Moderate Systemic Lupus Erythematosus

Inclusion Criteria: Part A (Healthy Participants) * Participant must be willing/able to adhere to the study visit schedule and other requirements, prohibitions, and restrictions specified in this protocol * Participant must have a body weight in the range of 50 to 90 kilogram (kg), inclusive, and have a body mass index (BMI) of 18 to 30 kilogram per square meters kg/m\^2, inclusive, at screening * Participant must be healthy on the basis of physical examination, medical history, vital signs, and 12-lead electrocardiogram (ECG) performed at screening. The determination that there is no evidence of active underlying illness by physical examination must be recorded in the Participant's source documents and initialed by the investigator * Participant must be healthy on the basis of clinical laboratory tests performed at screening * Before randomization, a woman must be: Not of childbearing potential: postmenopausal (\>45 years of age with amenorrhea for at least 12 months or any age with amenorrhea for at least 6 months and a serum follicle stimulating hormone (FSH) level \>40 international units per liters (IU/L) or mIU/mL); permanently sterilized (e.g., bilateral tubal occlusion \[which includes tubal ligation procedures as consistent with local regulations\], hysterectomy, bilateral salpingectomy, bilateral oophorectomy); or otherwise be incapable of pregnancy * A woman must agree not to donate eggs (ova, oocytes) for the purposes of assisted reproduction during the study and for 4 months (\>= 5 half-lives) after receiving last dose of study agent * A man who is sexually active with a woman of childbearing potential and has not had a vasectomy must agree to use a barrier method of birth control e.g., either condom with spermicidal foam/gel/film/cream/suppository or partner with occlusive cap (diaphragm or cervical/vault caps) with spermicidal foam/gel/film/cream/suppository, and all men must also not donate sperm during the study and for 4 months (\>=5 half-lives) after receiving the last dose of study agent Part B (Participants with Systemic Lupus Erythematosus) * Participant must be willing/able to adhere to the study visit schedule and other requirements, prohibitions, and restrictions specified in this protocol * Participant must have a body weight in the range of 40 to 100 kg, inclusive, and have a BMI of 18 to 30 kilograms per square meters (kg/m\^2), inclusive, at screening * Must meet Systemic Lupus International Collaborating Clinics (SLICC) criteria for diagnosis of lupus Exclusion Criteria: Part A (Healthy Participants) * Coexisting medical conditions or past medical history: Participant currently has or has had a history of any clinically significant medical illness or medical disorders the investigator considers significant should exclude the participant, including (but not limited to), neuromuscular disorder, hematological disease, immune deficiency states, respiratory disease, cardiovascular disease (including poor peripheral venous access), hepatic or gastrointestinal (GI) disease, neurological or psychiatric disease, ophthalmological disorders, neoplastic disease, renal or urinary tract diseases, or dermatological disease. Careful consideration should be given to whether the participant has had severe, progressive, or uncontrolled hepatic, hematological, gastrointestinal, endocrine, pulmonary, cardiac, neurologic/ cerebral, or psychiatric disease, or current signs and symptoms thereof * Participant has a condition that might confound assessments including major surgery, substance abuse or acute illness * Participant is a woman of childbearing potential or a woman who is pregnant, or breast-feeding, or planning to become pregnant while enrolled in this study or within 4 months (\>=5 half-lives) after the last dose of study agent Part B (Systemic Lupus Erythematosus \[SLE\] ) * Participant with history or suspected occurrence of drug-induced SLE * Participant has active Central nervous system (CNS) lupus or history of severe CNS lupus including but not limited to seizures, psychosis, transverse myelitis, CNS vasculitis and optic neuritis * Participant currently has or has had a history of any clinically significant medical illness or medical disorders the investigator considers significant should exclude the Participant, including (but not limited to), neuromuscular disorder, hematological disease, immune deficiency states, respiratory disease, cardiovascular disease (including poor peripheral venous access), hepatic or gastrointestinal (GI) disease, neurological or psychiatric disease, ophthalmological disorders, neoplastic disease, renal or urinary tract diseases, or dermatological disease. Careful consideration should be given to whether the Participant has had severe, progressive, or uncontrolled hepatic, hematological, gastrointestinal, endocrine, pulmonary, cardiac, neurologic/ cerebral, or psychiatric disease, or current signs and symptoms thereof * Participant has had major surgery, (e.g., requiring general anesthesia) within 4 months before screening, or will not have fully recovered from surgery, or has surgery planned within 4 weeks prior to study agent administration or during the time the Participant is expected to participate in the study, or within 4 months (\>=5 half-lives) after the last dose of study agent administration * Participant has laboratory findings or biopsy results consistent with severe lupus nephritis