Artificial Intelligence (AI) is increasingly used in mainstream applications to make decisions that affect a large number of people. While research has focused on involving machine learning and domain experts during the development of responsible AI systems, the input of lay users has too often been ignored. By exploring the involvement of lay users, our work seeks to advance human-centric responsible AI development processes. To reflect on lay users’ views, we conducted an online survey of 1,121 people in the United Kingdom. We found that respondents had concerns about fairness and transparency of AI systems, which requires more education around AI to underpin lay user involvement. They saw a need for having their views reflected at all stages of the AI development lifecycle. Lay users mainly charged internal stakeholders to oversee the development process but supported by an ethics committee and input from an external regulatory body. We also probed for possible techniques for involving lay users more directly. Our work has implications for creating processes that ensure the development of responsible AI systems that take lay user perspectives into account.