Reliable laboratory networks are fundamental to global health security because they generate the evidence required for disease detection, clinical management, antimicrobial-resistance surveillance, pathogen characterization, and public health response. Although molecular diagnostic technologies have expanded considerably, their effectiveness is frequently constrained by weak quality management systems, fragmented specimen-referral pathways, inadequate workforce competence, limited data interoperability, unstable supply chains, and insufficient biosafety and biosecurity controls. This paper examines the integration of laboratory quality management and molecular diagnostics within national and regional laboratory networks. A structured integrative review of international standards, technical guidance, and peer-reviewed empirical studies was undertaken. Quantitative evidence demonstrates that structured quality-improvement programmes can produce substantial gains. Across 302 laboratories completing the Strengthening Laboratory Management Toward Accreditation programme, average audit performance increased from 39% to 64%. Seven Kenyan blood-transfusion facilities improved from 38% at baseline to 79% at exit assessment. Electronic laboratory information-system implementation across 21 laboratories in Cote d'Ivoire produced an immediate 5.27-fold improvement in result timeliness and a 3.59-fold improvement in data completeness. Laboratory-network modelling in Kenya reduced estimated molecular drug-resistance testing turnaround time from approximately 8.5 working days under a centralized model to between 1.13 and 2.11 days under a hub-based model. These findings show that diagnostic technology produces maximum public health value only when integrated with governance, standardized quality processes, specimen referral, information systems, workforce development, biorisk management, and resilient procurement. An integrated laboratory-network framework and performance-monitoring model are proposed to support sustainable national preparedness and coordinated international response.