Block-wise semi-autoregressive decoding is the standard inference paradigm for diffusion large language models (DLMs), but it imposes a strict dependency between blocks: the next block cannot begin until the current block is fully decoded or its denoising budget is exhausted. We observe that once a block exposes a reliable delimiter boundary or stable semantic prefix, continuation generation need not wait for every residual token to be resolved. We propose AsyncLane, a training-free decoding scheduler that decouples refinement from advancement. AsyncLane forks a generate lane at observed delimiter boundaries into a refine lane and a continuation generate lane: the prefix remains editable, while the continuation advances before prefix refinement finishes. The resulting lane tree records decoding dependencies and output order, while execution proceeds over the active lane set. To make this asynchronous schedule efficient under bidirectional attention, AsyncLane combines shared-prefix lane batching, lookahead draft reuse, cascading termination, and compact cache refresh with refresh-logit reuse, preventing model-call cost from scaling directly with the number of lanes. AsyncLane is a drop-in replacement for block-wise DLM samplers and requires no retraining. Experiments on mathematical reasoning and code generation show that AsyncLane consistently improves throughput while maintaining competitive quality. Across LLaDA and Dream backbones, AsyncLane achieves the highest TPS in all evaluated benchmark-length settings; relative to the fastest competing baseline, it reaches peak speedups of 2.95x on LLaDA and 3.04x on Dream, with especially large gains under longer generation budgets.