Accurate segmentation of individual tree crowns (ITCs) from remote-sensing imagery is essential for forest monitoring and ecological analysis, yet remains challenging due to overlapping canopies and structural variability. The Segment Anything Model (SAM) shows strong generalization capabilities but requires effective prompting and domain adaptation for remote sensing applications. In this study, we investigate a lightweight fine-tuning strategy using Low-Rank Adaptation (LoRA) to adapt SAM for ITC segmentation on the BAMFORESTS dataset. The impact of different prompting strategies is evaluated, including manually annotated point and bounding box prompts, as well as automatically generated bounding boxes derived from a pre-trained tree detector. SAM is fine-tuned with instance-level ITC masks, enabling prompt-aware segmentation of multiple tree crowns per image. Performance is assessed before and after fine-tuning using standard instance segmentation metrics, including IoU and F1-score. Results show that LoRA-based adaptation improves mask delineation and robustness to prompt variability, with bounding box prompts consistently outperforming point-based inputs. Automatically generated prompts enable a fully automated workflow, although their effectiveness depends on detection quality. Evaluation on an independent validation site with manually annotated ITC labels shows that the fine-tuned LoRA-SAM model achieves performance comparable to manual annotations, while significantly reducing annotation effort. These findings highlight the importance of prompt design in adapting foundation models for remote sensing tasks and demonstrate that parameter-efficient fine-tuning provides a practical pathway toward scalable ITC segmentation.