In recent years, Transformer-based large language models (LLMs) have significantly improved upon their text generation capability. Mental health is a serious concern that can be addressed using LLM-based automated mental health counselors. These systems can provide empathetic responses to individuals in need while considering the negative beliefs, stigma, and taboos associated with mental health issues. Considering the large size of these LLMs makes it difficult to deploy these automated counselors on low cost/resource devices such as edge devices. Therefore, the motivation of the present study to analyze the effectiveness of lightweight LLMs in the development of automated mental health counseling systems. In this study, lightweight open source LLMs such as Google's T5 (small variant), BART (base variant), FLAN-T5 (small variant), and Microsoft's GODEL (base variant) have been fine-tuned for automated mental health counseling task utilizing a diverse set of datasets publicly available online. The experimental results reveal that BART's base variant outperformed the other models across all key metrics such as ROUGE-1, ROUGE-2, ROUGE-L, and BLEU with scores of 0.4727, 0.2665, 0.3554, and 25.3993 respectively. In comparison to other models, BART-base model generated empathetic, and emotionally supportive responses. These findings highlight the potential of lightweight LLMs (small size LLMs), in advancing the field of LLM-based mental health counseling solutions and underscore the need for exploration of lightweight LLMs for this mental health counseling use case. The code for this work is available at the following link: https://github.com/diviitmg03/Comparative-analysis-of-LLMs-.git .