Troubleshooting

The preview shows entries but the storefront shows nothing

Check you added .value to the metafield path. shop.metafields.lists.handle is the metafield object; .value is the array.
Check the handle. The key is the list's handle, shown in the editor, not its name.
Check the context. A per-product list is on product.metafields, not shop.metafields, and only on products that at least one matching entry references.
Storefront pages are cached. Wait a minute and reload.

A bound block in the theme editor is empty

The template JSON must read "{{ product.metafields.lists.handle.value }}", with .value.
Store-wide lists cannot be dynamic sources. Shopify does not allow shop metafields there. Read them in Liquid instead.
The block's setting must be of type metaobject_list, and it shows at most 50 entries.

Only 50 entries render

Liquid exposes only the first 50 entries of a list metafield, whatever you do with offset, reversed or index access. Make further lists with an offset in the app, one metafield each. See the Liquid reference.

The list is out of date

Changes normally arrive within fifteen seconds. If a list is stale:

Open the app. If it has not received webhooks for a while, it checks them on open and re-registers any that are missing.
Choose Sync now on the home page. This re-syncs every type and rewrites every list whose result changed.
If a specific type never updates, open a list on that type and save it again. Saving re-registers the type's webhooks.

The nightly sweep catches anything missed.

A list is marked "needs attention"

A field used by the list no longer exists on the type, or a referenced entry used in a condition was deleted. Open the list; the banner names the problem. Fix the condition and save. Until then the last written result stays in place.

Import skipped a list

The message names the missing type or field on the target store. Create it under Settings › Custom data › Metaobjects with the same handle and key, then import again with Overwrite ticked.

The preview and the saved result differ

The preview evaluates against the copy at that moment; the saved result is what was written at save time. If entries changed in between, save again. If the preview includes drafts and the saved list does not, check Include drafts.

I uninstalled and the lists are still on my products

That is intended. The metafields and their definitions stay so nothing breaks in the theme. Remove the definitions under Settings › Custom data › Products and Collections if you want them gone.

Something else

Email support@fourmileapps.com with the store domain, the list handle, and what you expected to see.