Existing LLM-based EDA agents are often isolated task-specific systems. This leads to repeated engineering effort and limited reuse of successful design and debugging strategies. We present LEGO, a unified skill-based platform for front-end design generation. It decomposes the digital front-end flow into six independent steps and represents every agent capability as a standardized composable circuit skill within a plug-and-play architecture. To build this skill library, we survey more than 100 papers, select 11 representative open-source projects, and extract 42 executable circuit skills within a six-step finite state machine formulation. Circuit Skill Builder automates skill extraction with linear scalability. Agent Skill RAG achieves submillisecond retrieval without relying on embedding models. Empirical evaluation on a hard subset of 41 VerilogEval v2 problems that gpt-5.2-codex fails to solve under extra-high reasoning effort shows that individual circuit skills constructed within LEGO raise Pass@1 from 0.000 to 0.805. This is an 80.5% gain over the baseline. Cross-project skill compositions also reach 0.805 Pass@1. They outperform hierarchy-verilog by 14.6% and VerilogCoder by 2.5%. They also match MAGE. These results show that modular skill composition supports both effective and flexible RTL design automation. The LEGO platform and all circuit skills are publicly available at GitHub: https://github.com/loujc/LEGO-An-LLM-Skill-Based-Front-End-Design-Generation-Platform