In this study, researchers will learn more about a study drug called BIIB059 (litifilimab) in participants with cutaneous lupus erythematosus (CLE). The study will focus on participants who have either active subacute CLE or chronic CLE, or both. They may also have systemic lupus erythematosus (SLE). The participants did not respond to antimalarial therapy or had problems with the treatment that made it hard to continue. The study will enroll only those participants who have completed treatment with litifilimab in the parent study, 230LE301. The main objective of the study is to learn more about the long-term safety of litifilimab. The main question researchers want to answer is: \- How many participants have adverse events and serious adverse events after taking litifilimab? Adverse events are unwanted health problems that may or may not be caused by the study drug. Researchers will also learn more about the effect of litifilimab on CLE. They will do this by measuring the symptoms of CLE over time using a variety of scoring tools. These include the Cutaneous Lupus Erythematosus Disease Area and Severity Index (CLASI), the Cutaneous Lupus Activity of Investigator's Global Assessment-Revised (CLA-IGA-R), and the SELENA-SLEDAI Flare Index (SFI). Researchers will look at how litifilimab and CLE affect the quality of life of participants using a group of questionnaires. They will also look at how litifilimab affects laboratory tests and how participants' immune systems respond to litifilimab. The study will be done as follows: * The last visit of parent study 230LE301 will be the first visit of study 230LE305. * All participants will receive litifilimab as an injection under the skin once every 4 weeks. Both researchers and participants will know the dose and identity of the study drug. * Globally, the treatment period will last up to 104 weeks, or 2 years. For participants in the United States, the treatment period may last up to 260 weeks, or 5 years * There will be a follow-up safety period that lasts up to 24 weeks. * Globally, participants will have up to 27 study visits during the treatment period. In the US, participants will have up to 66 study visits. * Globally, the total study duration for participants will be up to 128 weeks. In the US, the total study duration will be up to 284 weeks .