Just for a moment, forget all what you know about agile and lean. Forget about all the agile methodologies, frameworks and other agile concepts out there. Useful as they might be, they can impede getting into the spirit of true agility.
What matters most
First and foremost, it's critical to be clear about your vision and mission in life, as organization and as individual. When it's not clear yet, take some time pondering and contemplating about those essential questions. Really make sure they are close to your heart and are aligned with the underlying intent of the spirit of the organization. Formulate your vision and mission carefully. Be honest as well.
Honesty can shine light upon the real intentions - which are maybe considered not to be that pure or philanthropic as Mother Theresa - which can be scary. The more honest you are about your intentions and the resulting mission and vision - as individual and organization - the more strongly focused and motivated the organization can and will be as a whole. The parts of the organization which are not in alignment with the organization's vision and mission are better of somewhere else, for both's sake.
What matters most to any organization is realizing its vision by pursuing its mission and objectives. All that positively affects this journey is very much welcomed. All that jeopardizes this journey is discarded.
Ideally this consideration should be the critical factor for making any decision or performing an action. Behaving in such a way which positively affects the pursuit of its mission should be a matter of course and commonsense throughout the organization - within the agreed upon organization's ethics.
Ideally all parts of the organization are aligned with its vision, mission and ethics. All parts of the organization ideally are as much involved as any other part. Every part is aiming to have a positive impact of realizing the vision of the organization. Each and every part knows best what to do from its location/perspective in the organization and is fully empowered to act. The part is the organization, albeit diversified across multiple parts.
This is what being truly agile is about. To be - as a part of the whole - in the knowing what is the best way forward (leveraging skillful means) from any given circumstance and to be fully empowered to act. No need to ask for approval to perform whatever action - you know best as you are fully aligned with the underlying spirit of the organization (intent, vision, mission). No outside stimulans is needed, nor is it helpful because this negatively affects agility. No external authority is present, nor accepted, as the only recognized authority is inside.
Moving to the ideal
This ideal seems quite a stretch away from where most organizations are at the moment. Yet, this is where agility is ultimately heading to, even though it might seem as a far away future landscape from our current position.
Developing higher levels of awareness is the key to be able - as part of the whole and as a whole - to attain this ideal and true agility. Awareness of one's self (self-awareness), one's effect on its surroundings and awareness of the intrinsic connection between the inner and outer world. Awareness is essential in the described ideal and can't be neglected. Without awareness it's impossible to align intent, vision and mission with the parts of the organization and the organization as a whole. True agility can't be embodied without alignment.
Training oneself and the organization is a start, but cultivating (self-)awareness isn't a one-time-thing. It requires continuous practice and attention. Cultivating and developing awareness to ever higher extent should become intrinsically interwoven into the daily operations of an organization - not as an add-on, which is a result of compartmentalized thinking and is antagonistic to gaining awareness. Mindfulness practices are of great importance on the journey of ever developing awareness.
Animation and incubation
Agile thinking is primary and needs incubation time to reflect in behavior. A certain mentality and spirit needs to be present and all-pervasive in the organization - the organization needs to be infused with the spirit of true agility. The spirit of true agility needs to be animated and embodied throughout the organization.
Every organization is unique and therefore requires an unique and agile approach to gain ever higher levels of agility on the path to reaching the state as described in the ideal. Help can be provided from outside of the organization - in the form of guidance, consultancy or leveling/coaching - but the only one who is able to know yourself is you, on the inside of the organization.
Know thyself from the inside, not the outside.