what is difference between BASE and FOUNDATION in terms of figurative meaning
EX : He laid the BASE/FOUNDATION of Japan's modern economy
Foundations, literally, are the structure below the surface of the ground on which buildings are then constructed. The word is often used figuratively for something which represented the founding of something greater.
The base of something, literally, is the lowermost part on which it sits. It isn't the same as a foundation. The base of something can be movable whereas a foundation is generally immovable.
Some people, even native English speakers, use the expression "lay the base" incorrectly - it should be "lay the basis". You will see from the link that this correct expression is interchangeable with 'lay the foundation' and can be used in the same figurative sense. The 'basis' of something is the most important facts, ideas, etc. from which that thing is developed.
In many cases, there is no big difference between base (or basis) and foundation when used figuratively.
However, in your example, you need to use foundation. This is because the correct phrase is lay the foundation, not lay the base.