Before updating the payment date of an invoice, you can have a look at this article to understand how payments are managed in LSP.expert: https://help.lsp.expert/en/articles/7063548-how-can-i-manage-the-payment-s-of-my-invoices.

To edit the payment date of an invoice, you have to update the latest payment entry in the invoice, using the Payments panel on the right.

Click on the three dots next to the payment entry and click on Edit. Then, simply edit the payment date and click on Save.