Hidradenitis suppurativa (HS) and atopic dermatitis (AD) are chronic inflammatory skin diseases that lead to the development of skin lesions and symptoms such as pain and discomfort. The purpose of this study is to assess molecular changes in adult participants with moderate to severe HS or with moderate to severe AD. Lutikizumab (ABT-981) is an investigational drug being developed for the treatment of HS and AD. This study will consist of 2 sub-studies: Sub-Study 1 moderate to severe hidradenitis suppurativa and Sub-Study 2 moderate to severe atopic dermatitis. Approximate 60 participants will be enrolled in the study at approximately 2 sites in the US. In Sub-Study 1 HS participants will receive subcutaneous (SC) injections of lutikizumab for up to week 15 with a 70-day follow-up period. In Sub-Study 2 AD, participants will receive subcutaneous (SC) injections of lutikizumab for up to week 14 with a 70-day follow-up period. The study duration for Sub-Studies 1 and 2 is expected to last up to 30 weeks. Participants in Sub-Study 1 (HS) who complete Week 16 and showed a therapeutic benefit to lutikizumab, as confirmed by the investigator, will have the option to enter an open-label long-term extension (LTE) to continue to receive lutikizumab for up to an additional 140 weeks, followed by a 70-day follow-up period. 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 and may require frequent medical assessments, blood tests, and biomarker collections.