Large language models (LLMs) have revolutionised many fields, with LLM-as-a-service (LLMSaaS) offering accessible, general-purpose solutions without costly task-specific training. In contrast to the widely studied prompt engineering for directly solving tasks (in vivo), this paper explores LLMs' potential for in-vitro applications: using LLM-generated labels to improve supervised training of mainstream models. We examine two strategies - (1) noisy label correction and (2) training data augmentation - in empathy computing, an emerging task to predict psychology-based questionnaire outcomes from inputs like textual narratives. Crowdsourced datasets in this domain often suffer from noisy labels that misrepresent underlying empathy. We show that replacing or supplementing these crowdsourced labels with LLM-generated labels, developed using psychology-based scale-aware prompts, achieves statistically significant accuracy improvements. Notably, the RoBERTa pre-trained language model (PLM) trained with noise-reduced labels yields a state-of-the-art Pearson correlation coefficient of 0.648 on the public NewsEmp benchmarks. This paper further analyses evaluation metric selection and demographic biases to help guide the future development of more equitable empathy computing models. Code and LLM-generated labels are available at https://github.com/hasan-rakibul/LLMPathy.