XSD Element Not Null or Empty Constraint For Xml?

Try

<xs:element name="lastName" minOccurs="1" nillable="false">
  <xs:simpleType>
     <xs:restriction base="xs:string">
       <xs:minLength value="1"/>
     </xs:restriction>
  </xs:simpleType>
</xs:element>

<xsd:element name="lastName" type="NonEmptyString" nillable="false"/>

<xsd:simpleType name="NonEmptyString">
  <xsd:restriction base="xs:string">
    <xsd:minLength value="1" />
    <xsd:pattern value=".*[^\s].*" />
  </xsd:restriction>
</xsd:simpleType>