<p>Governments increasingly deploy algorithmic and AI-enabled systems in welfare administration, fraud detection, eligibility determination, and frontline service delivery. As these systems become embedded in routine public administration, agencies face rising expectations to sustain procedural fairness, accountability, and transparency throughout system development and long-term operation. Recent public-sector failures suggest that governance responsibilities are frequently fragmented across organizational units and unevenly enacted over time, enabling administrative harms to emerge without clear attribution of responsibility. This paper synthesizes and operationalizes a lifecycle-aligned governance indicator framework that treats AI governance as an institutional responsibility sustained across key phases of the AI development lifecycle. Drawing on established debates in algorithmic public administration, the framework organizes governance dimensions, including accountability and oversight, data governance, fairness and transparency practices, and post-deployment monitoring, into phase-specific and evidence-oriented indicators. Each indicator specifies the expected administrative artifacts that may support qualitative assessment, such as role assignment records, data documentation, assessment records, transparency disclosures, and monitoring logs. In this way, the framework supports traceable governance interpretation rather than a static compliance checklist, numerical scoring model, or formal audit determination. We use two public-sector cases as illustrative applications to examine how publicly reported information can be organized in relation to phase-specific governance responsibilities and potential governance concerns. This work offers a structured, evidence-oriented lens for public-sector lifecycle assessment, while recognizing that the framework does not provide causal validation, formal audit findings, universal applicability, or comprehensive governance coverage across AI domains.</p>