Accurate lesion segmentation underpins automated dermoscopic analysis: masks enable measurements of asymmetry, border and size. Deployment in primary care or on mobile devices requires a compact network. Existing ultra-light Mamba U-Nets offer global context, but global-modeling cost depends on each Mamba block's resolution, while their local branches rely on a single square kernel. We introduce LCM-UNet, a 33,474-parameter U-shaped network that fuses every skip at its native resolution, restricts bidirectional Mamba to stages at one-sixteenth of the input resolution or coarser, and uses local convolutions at finer scales. A multi-basis reparameterizable adapter augments each local branch during training with dilated, horizontal and vertical depthwise kernels, then folds them into the host kernel before inference. Each skip connection also learns a stage-specific gain. Nine networks were retrained on the official ISIC 2017 and ISIC 2018 partitions under a harmonized protocol, with PH
2 reserved for external validation and ablations run on a development split. LCM-UNet achieved Dice scores of 88.62%, 89.73% and 90.46% on ISIC 2017, ISIC 2018 and PH
2, respectively, ranking first on both ISIC test sets and second on PH
2 among the compared models. In the native-resolution host, removing Mamba from the one-eighth-resolution decoder stage eliminated 63% of Mamba operations, corresponding to 5.3% of all operations, with a Dice change of
−0.03 percentage points. The adapter improved Dice by 0.48 percentage points over a single host kernel without adding deployed parameters or operations. With latency so far measured only on a GPU, LCM-UNet is a candidate for resource-constrained deployment.