Every person, firm or corporation who, under and by virtue of a contract with such general contractor as is mentioned in section one of this article, or with a subcontractor for a part of such work, either for an agreed contract price or by day or by piece, or other basis of payment, shall furnish any part of the materials, machinery or other necessary supplies or equipment, or shall perform any labor, do any work or provide any services necessary to the completion of any general contract, such as is mentioned in section one of this article, shall have such a lien for his or her compensation, as is provided for in section one of this article.