Demand response (DR) is central to innovative grid efforts, yet traditional models often neglect social equity. We present a Fairness-First DR algorithm that embeds energy justice principles, digital inclusion, and algorithmic accountability into load-shifting strategies. Using Jaipur, India, as a case study, we propose a conceptual model that balances utility goals, such as peak reduction, with justice-oriented aims, including affordability, participation, and recognition. Our framework expands conventional energy models by integrating equitable DR access regardless of device ownership or internet access. We synthesise demand data under a cost-minimising baseline and our Fairness-First controller. Results show significantly improved equity, as low-income households capture a greater share of bill savings, and the Jain fairness index rises from 0.65 to 0.92, with minimal loss in peak reduction. Informal dialogue with Jaipur stakeholders - policymakers, utility engineers, and residents - reveals strong concern about fair benefit-sharing. Residents frequently worry that DR programs may favour those with smart appliances, excluding poorer households. We outline a realistic implementation pathway through Indian institutions, including the Ministry of New and Renewable Energy (MNRE), the Energy and Resources Institute (TERI), the Self-Employed Women's Association (SEWA), and state governments. Proposed solutions address key barriers to peak reduction, including digital literacy, data gaps, and trust, by providing training and promoting transparent data sharing. By placing justice at the heart of DR, this study contributes actionable insights for more equitable energy transitions.