Lean:
Lean has its origins in the Toyota Production System. There, for me, it is then the focus on "Kaizen" (continuous improvement) and "Muda" (one of the avoidance principles to identify and stop doing things that waste time). Of course, other aspects are also part of it. Still, most of the themes, such as "Best Quality" or "Lowest Cost" pay into Kaizen and Muda.
Agile:
Agile existed before the agile manifesto, but for me this one highlights a few key aspects. The Scrum Guide describes the three pillars of agility as "transparency", "inspect" and "adapt": make what you do visible and adapt your approach in small cycles after you have questioned it.
But in which direction do I question my approach? What is the goal of the adjustments?
That's the lean idea for me. Check if what you are doing is the right thing. Are you wasting time? Where can you improve? So act in the spirit of Kaizen and Muda.
So it was obvious to me to combine them in one slogan.
Think lean, act agile!