ISO has a fundamental for business. their mission for quality, can adopt lean manufacturing to help improve internal processes and productivity ?

As Salam,

If you meant ISO Qualilty management system by ISO it is only for a system description & standard for quality management. But Lean is a deep culture for continious improvement and basicly a system to eliminate wastes, increase the value added time.

Moreover, about your question ; Lean is extremely involved with improving internal processes and productivity. Without adoption ISO and Lean we can not develope our organization. Thinking them seperately causes only conflict in the company. Some people with Lean and others are against of lean supporter of ISO!

ISO defines standards and effective steps to reach at managing quality system. Surely the items of ISO requires higher quality and productivity as the understanding of "Being Result Oriented" and it suggest using Lean methodologies as an asset.

ISO is only business principal, BUT lean manufacturing is something else. 

ISO is only business principal, BUT lean manufacturing is something else. (i.e. ISO asked for continual improvement - and lean manufacturing tell us the methods and tools for the improvement of internal process and productivities)

In my opinion, ISO9001 focuses on quality, making sure that quality product is delivered through process control, workers competency etc.  However, it does not guide the organization to have better productivity, efficiency and less wastage.

So, you should adopt lean for what it is, waste elimination.  So your processes will not only ensure quality products, but would try to be as efficient as possible in achieving it.  More efficient here not only less cost, but also can be increased productivity.

ISO is just documented, depending on collecting data and analyting them. Lean is actions done or will be done to solve all problems found.

Do ISO9001 supports lean , or lean supports ISO based on their orgnal principles.....my answer is yes ...

Lean does help ISO9001 to be truly a part of the organization’s management system. also ISO can actually help sustain the gains of a lean implementation. 

How it is possible ,

As ISO9001 can help sustain kaizen activities

ISO9001 repeats86 times that the goal is “effective and efficient” processes. It is not incompatible at all with the search for waste    

Example: if materials are transported more than strictly necessary (process waste), there is a risk they they get damaged or lost (quality problems).

-When process waste  (apart from defects) is observed, a preventive action plan can be prepared. The reason is simple: these types of waste (transportation, inventory, unnecessary motion, waiting, over-processing, over-production) generally make operations less likely to satisfy the customer. 

-When defects are observed, a corrective action plan is to be prepared.

Finally I can say , one should extent by adding some5S assessment forms, kanbans, and other lean documents in the quality management system is perfectly fine. ISO9001 should be seen as guidance for a good “business management system” — it is not just about quality.