Take it home and re-core it.
Common problem on quite a few middle aged boats. As long as the surface is OK, the hidden underside can be easily repaired.
When you cut/grind out the old coring, do keep that lid supported to maintain the surface curvature.
Some West System epoxy, thickener, some new coring, and a layer of 'biax' cloth to finish off.
There are web sites and videos to help, and do get the instructional material from West Systems.
(If you find a used one, it will likely have core issues, too...)