xmllint validation error "no DTD found" while using XSD

--valid is for DTDs, not XSDs.

This will work for you instead:

xmllint --noout --schema http://lucas.ucs.ed.ac.uk/xml-schema/xmlns/simple.xsd lucas-basic.xml

The OP attempt and accepted answer "validate" the XSD by testing it against a sample file. To validate the XSD file against the XSD specification, the following command may be used:

xmllint --noout --schema http://www.w3.org/2001/XMLSchema.xsd my_schema.xsd

... and for v1.1 the schema is https://www.w3.org/2009/XMLSchema/XMLSchema.xsd

NOTE: the v1.0 schema has some qualifications at the top about the normative structure schema so it's possible another file should actually be used but this worked fine for me.