How can I change the XML Encoding when writing XML data

The encoding written into the XML document and the actual encoding of the XML data are determined by the Writer passed into the Serialize method of LxSerializer.

For example, if a .Net XmlWriter is used, then you can specify the encoding using XmlWriterSettings:
MyElementClass elmCls = ...;
XmlWriterSettings xws = new XmlWriterSettings() { Encoding = Encoding.Unicode };

using (XmlWriter writer = XmlWriter.Create("MyXmlFile.xml", xws))
{
    serializer.Serialize(writer, elmCls);
}

Whereas, if a StreamWriter is used, the encoding can be set on the constructor:
MyElementClass elmCls = ...;

using (StreamWriter sw = new StreamWriter("MyXmlFile.xml", Encoding.Unicode))
{
    serializer.Serialize(writer, elmCls);
}

Note: If a StringWriter is used, the output will always be UTF-16 as this is how .Net stores strings internally.