Is ISO 17025 needed?

You said “We need to do test that requires that they are doing under a laboratory quality management system compliant to ISO 17025 or alike standards”

I do not have the background whether you are referring to testing medical devices and if you offer contract testing or internal testing of your own medical devices. I suggest you obtain some specific information from the party requiring this, as there are regulatory requirements related to medical devices.

As an overview, ISO 9001 is a general management system not applicable to provide assurance that a laboratory is competent to perform a particular test, from a technical perspective. The ISO 9001 requirements for management are included in ISO 17025, so with your ISO 9001 system certification you can implement the additional ISO 17025 requirements to work in accordance with ISO 17025 and thereafter achieve accreditation. ISO 17025 is specifically applicable to testing and calibration. Both ISO 17025 and ISO 13485 are competency-based standards with some overlap. Typically an medical device manufacturer does not need ISO 17025 accreditation, however when it comes to testing medical devices many of the ISO 71025 practices are beneficial.

For some more information on ISO 17025 see this Q&A reply and links within: https://community.advisera.com/topic/17025-vs-13485/