Carbon emission flow analysis in power systems provides crucial support for realizing panoramic electricity-carbon tracking and for implementing carbon-reduction strategies in real-world grids. The primary objective of carbon-emission-flow (CEF) analysis is to determine the nodal carbon intensity (NCI) of every bus from the power-flow solution. However, current methodologies exhibit poor scalability to large-scale power systems; traditional solvers cannot meet the stringent efficiency requirements and overlook the carbon emissions associated with network losses in practical grids. To address these shortcomings, we present an enhanced hybrid method that refines and seamlessly integrates the classical direct solver with a recursive-update scheme. Matrix sparsification is applied to the direct solver, while recursive refinement accelerates NCI computation; simultaneously, the NCI formulation is revised to explicitly incorporate loss-induced emissions. Comprehensive case studies on the IEEE 24-bus system and the Norwegian 2383-bus system benchmark the proposed method against two baselines, and time and space complexity, carbon-flow conservation, and measured CPU time and memory footprint. A lossy IEEE 30-bus system further validates the treatment of network losses. The resulting technique delivers efficient, feasible, and rapid CEF computation for real-world large-scale lossy power systems.