In JavaScript: Understanding the Weird Parts lexical environment is explained as the scope of your code while execution context is a collection of lexical environments, and that
Execution Context & Execution Context stack : Execution context is the internal javascript construct to track execution of a function or the global code. The js engine maintains a stack - execution context stack or call stack, which contains these contexts and the global execution context stays at the bottom of this stack. And a new execution context is created and pushed to the stack when execution of a function begins. A particular execution context tracks the pointer where statement of the corresponding function is being executed. An execution context is popped from the stack when corresponding function's execution is finished.
Lexical Environment : it's the internal js engine construct that holds identifier-variable mapping. (here identifier refers to the name of variables/functions, and variable is the reference to actual object [including function type object] or primitive value). A lexical environment also holds a reference to a parent lexical environment.
Now, for every execution context -- 1) a corresponding lexical environment is created and 2) if any function is created in that execution context, reference to that lexical environment is stored at the internal property ( [[Environment]] ) of that function. So, every function tracks the lexical environment related to the execution context it was created in.
And every lexical environment tracks its parent lexical environment (that of parent execution context). As a result, every function has a chain of lexical environments attached to it. [Note: in js a function is an object, creating a function by a statement means creating an object of type Function. So like other objects, a function can hold properties both internal and user defined]
The js engine search any variable or function identifier in the current lexical environment, if not found it searches the chain attached to the enclosing function. (for global code this chain does not exist). So, you understand how scoping of variables and functions are maintained. The concept of closure is also backed by, this chain (not a standard term, I just used it to ease the understanding). When a function instance is passed to another function as an argument, to be used as callback, it carries it's chain with it (sort of).
Note: the answer is based on what I learned from 'Secrets of the Javascript Ninja, 2/e'