How to bind the lightbox default save button and delete button with the interface to add, modify and delete the corresponding data in the database

For example:
Click the default save button of the light box to add or update relevant data in the database

Hello,
Gantt is a client-side library, it doesn’t directly communicate with the database or the server-side. All changes occur only inside the browser.

To load the data, you can use the gantt.load or gantt.parse methods:
https://docs.dhtmlx.com/gantt/api__gantt_load.html
https://docs.dhtmlx.com/gantt/api__gantt_parse.html

To send the changes to the server, you need to use the Data Processor or built-in Ajax module. You can read more about it in the following articles:
https://docs.dhtmlx.com/gantt/desktop__server_side.html
https://docs.dhtmlx.com/gantt/api__gantt_ajax_other.html

Here are examples:
http://snippet.dhtmlx.com/41d5ffad3
http://snippet.dhtmlx.com/5/d0b0020f8

However, if you have ready methods to edit the database, you can redefine the lightbox button actions by using the event handlers:
https://docs.dhtmlx.com/gantt/api__gantt_onlightboxsave_event.html
https://docs.dhtmlx.com/gantt/api__gantt_onlightboxdelete_event.html
https://docs.dhtmlx.com/gantt/api__gantt_onlightboxcancel_event.html
https://docs.dhtmlx.com/gantt/api__gantt_onlightboxbutton_event.html

And you can create a modal that will look like the lightbox:
http://snippet.dhtmlx.com/5/69a2068a1