ISO 17025 first steps

It does not make a difference if the laboratory has its own ISO 9001 certification or the entire facility has ISO 9001 certification, which includes the laboratory. The laboratory will, as an organisation, only have ISO 9001 certification.  ISO 17025:2017 international standard accreditation requires more of a laboratory than just meeting the requirements of a quality management system (such as 9001).  It is conformity assessment standard where the technical and overall competence of the laboratory is established, peer-assessed, confirmed and recognised by an accreditation body.

Have a look at the following expert answer ISO 9001:2015 vs ISO 17025 at  https://community.advisera.com/topic/iso-90012015-vs-iso-17025/ for further information on how ISO 9001 is integrated into ISO 17025 so the management requirements do not need to be re-addressed separately within ISO 17025.

Also have a look at the article ISO 17025 vs. ISO 9001 – Main differences and similarities for some more information, available at https://advisera.com/17025academy/blog/2019/07/11/iso-17025-vs-iso-9001-main-differences-and-similarities//