I've mocked this up and I can't repeat the problem.
Your code looks OK
xxx.DataWystawienia = LxDateTime.Today;
The code that does the conversion looks like this. So it looks like the value you are setting into DataWystawienia is a LxDateTime of type DateTime (Today returns an LxDateTime of type Date).
if (val.Type != LxDateTimeType.Date)
{
stringValue = "";
errorType = ConversionErrorType.FormatError;
errorMsg = $"The LxDateTime({val.Type}) could not be converted to a xs:date";
return false;
}
I've changed the code to make it automatically convert to the target LxDateTimeType if the conversion is possible.
if (val.TryChangeType(LxDateTimeType.Date, out LxDateTime date) == false)
{
stringValue = "";
errorType = ConversionErrorType.FormatError;
errorMsg = $"The LxDateTime({val.Type}) could not be converted to a xs:date";
return false;
}
But I think the problem is you are passing a LxDateTime of type DateTime into a property that expects a LxDateTime of type Date.