We present DiLemma, a novel approach to assisting automated inductive equational proofs through lemma discovery with recursive function synthesis. Inductive equational proofs play a crucial role in diverse domains, including the automated assessment of programming assignments and the verification of compiler correctness. However, a major challenge lies in discovering provable and applicable lemmas in stuck states, which often necessitate auxiliary functions to reconcile values of differing structures. To address this issue, we propose DiLemma, a lemma discovery framework that establishes provable lemmas while simultaneously synthesizing and employing auxiliary functions for data handling. DiLemma first identifies recurring patterns from sequences of stuck states, then synthesizes recursive functions based on these patterns, and finally formulates lemmas that integrate the synthesized functions with the corresponding states. Experimental results demonstrate that DiLemma achieves up to a 50% improvement in equivalence proving for introductory-level programs. We further plan to evaluate its effectiveness on benchmarks across a wider range of domains.