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By default locked items aren't included in XML serialization output, and there is no any public API to disable such behaviour, but you can add the next code after including all js files, but before tree initialization:

dhtmlXTreeObject.prototype._serializeLockItem=dhtmlXTreeObject.prototype._serializeItem;

This will solve your problem.

If you haven't found the needed information there and still looking for a solution, you will find the additional help checking editable grid php and the scheduler.