Low-resource languages pose persistent challenges for Natural Language Processing tasks such as lemmatization and part-of-speech (POS) tagging. This paper investigates the capacity of recent large language models (LLMs), including GPT-4 variants and open-weight Mistral models, to address these tasks in few-shot and zero-shot settings for four historically and linguistically diverse under-resourced languages: Ancient Greek, Classical Armenian, Old Georgian, and Syriac. Using a novel benchmark comprising aligned training and out-of-domain test corpora, we evaluate the performance of foundation models across lemmatization and POS-tagging, and compare them with PIE, a task-specific RNN baseline. Our results demonstrate that LLMs, even without fine-tuning, achieve competitive or superior performance in POS-tagging and lemmatization across most languages in few-shot settings. Significant challenges persist for languages characterized by complex morphology and non-Latin scripts, but we demonstrate that LLMs are a credible and relevant option for initiating linguistic annotation tasks in the absence of data, serving as an effective aid for annotation.