Hidradenitis suppurativa (HS) is a chronic and often painful inflammatory skin disease which includes the forming of lumps, abscesses and scars in areas of the skin such as under the breasts, under armpits, inner thighs, groin and buttocks. This study will compare lutikizumab versus placebo for the treatment of adult and adolescent participants with the signs and symptoms of moderate to severe HS . Lutikizumab is an investigational drug being developed for the treatment of HS. During Period 1 of the study, participants will placed in 1 of 2 groups called treatment arms. There is a 1 in 2 chance that participants will be assigned to placebo. Around 1280 adult and adolescent participants with moderate to severe HS will be enrolled in the study at approximately 275 sites world wide. During Period 2, participants that were part of the lutikizumab treatment arm in Period 1 will be re-randomized to 1 of 2 lutikizumab treatment arms. Participants that were part of the Placebo arm in Period 1 will start Period 2 with an initiation of lutikizumab followed by a re-randomization to 1 of 2 lutikizumab treatment arms. In Period 1, participants will receive subcutaneous injections of lutikizumab or placebo every week for 16 weeks. In Period 2, participants that were randomized to lutikizumab in Period 1 will receive subcutaneous injections of lutikizumab every week or every other week for 36-weeks. Participants that were randomized to the placebo arm in Period 1 will receive subcutaneous injections of lutikizumab every week for 16 weeks, then either every week or every other week for 20 weeks. Period 3 is the Long Term Extentsion (LTE) and through Week 68, participants will continue to receive lutikizumab SC using the same assigned dosing regimen from the end of Period 2 for 16 weeks followed by open-label lutikizumab EOW for 140 weeks. Participants in the US that complete Periods 1 \& 2 will have the option to enroll in a 156-week open-label Sub-Study that will assess the long term safety and efficacy of lutikizumab in a prefilled pen. There may be higher treatment burden for participants in this trial compared to their standard of care. Participants will attend regular visits during the study at a hospital or clinic. The effect of the treatment will be checked by medical assessments, blood tests, checking for side effects and completing questionnaires and diaries.