Is it possible for the company's internal lab to get ISO accreditation?

Yes indeed, any testing or calibration laboratory, irrespective of size can be accredited. In your case, the client is internal, I assume the production plant ? The benefits of accreditation apply for inhouse laboratories too. Some internal laboratories have larger risks to ensuring quality and safeguarding impartiality than commercial contract work laboratories, so this needs to be carefully addressed.

The following articles may be of interest:
Six key benefits of ISO 17025 implementation at https://advisera.com/17025academy/blog/2019/10/18/six-key-benefits-of-iso-17025-implementation/

What is ISO 17025? at https://advisera.com/17025academy/what-is-iso-17025/

Also have a look at similar topics in the 17025 Expert Advice Community

ISO 17025 for internal quality control laboratory at https://community.advisera.com/topic/iso-17025-for-internal-quality-control-laboratory/
Assuring impartiality and confidentiality (for an internal laboratory) at https://community.advisera.com/topic/assuring-impartiality-and-confidentiality/