Replay-free continual automatic speech recognition (ASR) requires adapting to new speech domains while maintaining a single persistent model without old data, task identifiers, or inference-time routing. We identify commit-stage update admission as a distinct post-training problem for continual low-rank adaptation (LoRA): after a task-wise LoRA update has been trained, the system must decide which part of that update should become persistent in the deployed model. This decision is especially important in ASR, where domains share phonetic and transcription structure but still differ in speakers, channels, noise, speaking style, and lexical coverage. We propose HarmoLoRA, a rank-constrained commit operator that decomposes the trained current-task update with respect to previously committed directions, constructs a rank-closed residual commit path, and uses a lexicographic constrained rule to choose the smallest residual admission coefficient among near-best realized candidates. The selected update is committed to one merged ASR checkpoint, requiring no replay, task identifiers, routing, gating, or multi-branch selection at inference. Across the reported ASR orders, HarmoLoRA improves recognition performance and reduces forgetting relative to reproduced replay-free and LoRA-based continual adaptation baselines.