Add Lychee Doc Links Check to Local and CI (#19742)

Co-authored-by: Zijie Xia <zijie_xia@icloud.com>
Co-authored-by: Zijie Xia <zijiexia@users.noreply.github.com>
Co-authored-by: zijiexia <37504505+zijiexia@users.noreply.github.com>

docs/performance_dashboard/index.html

@@ -936,7 +936,7 @@
             <p>
                 SGLang Performance Dashboard &mdash;
                 <a href="https://github.com/sgl-project/sglang" target="_blank">GitHub</a> &middot;
-                <a href="https://sgl-project.github.io/sglang" target="_blank">Documentation</a>
+                <a href="https://docs.sglang.io/" target="_blank">Documentation</a>
             </p>
         </footer>
     </div>