This paper addresses the problem of estimating causal directed acyclic graphs in linear non-Gaussian acyclic models with latent confounders (LvLiNGAM). Existing methods assume mutually independent latent confounders or cannot properly handle models with causal relationships among observed variables. We propose a novel algorithm that identifies causal DAGs in LvLiNGAM, allowing causal structures among latent variables, among observed variables, and between the two. The proposed method leverages higher-order cumulants of observed data to identify the causal structure. Extensive simulations and experiments with real-world data demonstrate the validity and practical utility of the proposed algorithm.