We introduce VL2NL, a Large Language Model (LLM) framework that generates rich and diverse NL datasets using only Vega-Lite specifications as input, thereby streamlining the development of Natural Language Interfaces (NLIs) for data visualization. To synthesize relevant chart semantics accurately and enhance syntactic diversity in each NL dataset, we leverage 1) a guided discovery incorporated into prompting so that LLMs can steer themselves to create faithful NL datasets in a self-directed manner; 2) a score-based paraphrasing to augment NL syntax along with four language axes. We also present a new collection of 1,981 real-world Vega-Lite specifications that have increased diversity and complexity than existing chart collections. When tested on our chart collection, VL2NL extracted chart semantics and generated L1/L2 captions with 89.4% and 76.0% accuracy, respectively. It also demonstrated generating and paraphrasing utterances and questions with greater diversity compared to the benchmarks. Last, we discuss how our NL datasets and framework can be utilized in real-world scenarios. The codes and chart collection are available at https://github.com/hyungkwonko/chart-llm.