In this study, researchers will learn more about a study drug called litifilimab (BIIB059) 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 main objective of the study is to learn about the effect litifilimab has on lowering the activity of the skin disease. Researchers will measure symptoms and signs 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). The main questions researchers want to answer are: * How many participants have a score of 0 or 1 on the CLA-IGA-R looking at skin redness after treatment? * How many participants have their skin disease activity go down by at least 70% as measured by CLASI? Researchers will also learn more about the safety of litifilimab. They will study how participants' immune systems respond to litifilimab. Additionally, they will measure the effect litifilimab and CLE have on the quality of life of participants using a group of questionnaires. The study will be split into 2 parts - Part A and Part B. Both parts will be done as follows: * After screening, participants will be randomized to receive either litifilimab or placebo for the 1st treatment period. A placebo looks like the study drug but contains no real medicine. * Participants will receive either litifilimab or placebo as injections under the skin once every 4 weeks. * The 1st treatment period will be double blinded which means neither the researchers nor the participants will know if the participants are receiving litifilimab or placebo. * This double blinded treatment period will last 24 weeks, after which the 2nd treatment period will begin. * During the 2nd treatment period, all participants will receive litifilimab for 28 weeks. * After completing treatment in this study, participants that qualify will be given the choice to join the Long-Term Extension study, 230LE305. If they do not, they will move into a follow-up safety period that will last up to 24 weeks. * The total study duration for participants will be up to 80 weeks.