My short answer: "c 'lambda-of' e". Although I am clinging to "'lambda' c 'function' e", I think lambda-of is the ecumenical compromise. Analysis follows.
This is a great question if only for the bizarre answers. Most of the translations have other meanings than for lambda expressions, leading to exotic interpretations. As an old lambda-expression hacker, I just ignore the .NET notation and rewrite it as lambda in my head while wishing they had done almost anything else for this.
For narrating code over the phone, you want someone to be able to write the code down in sequence. That is a problem, of course, but lambda-arrow or something is probably the best you can get, or maybe lambda-in, but lambda-of is the most accurate.
The problem is the infix usage and how to name the whole thing and the role of the left and right parts with something that works when spoken in the infix place.
This may be an over-constrained problem!
I wouldn't use "such that" because that implies that the right hand side is a predicate that the left-hand side should satisfy. That is very different from talking about a right-hand side from which the left-hand side has been abstracted as a functional parameter. (The MSDN statement about "All lambda expressions" is simply offensive as well as inaccurate.)
Something rankles about "goes to" although it may be as close as we can get. "Goes to" implies a transformation, but there is not exactly some variable c that goes to an expression in c. The abstraction to a function is a little elusive. I could get accustomed to this, but I still yearn for something that emphasizes the abstraction of the variable.
Since the left-hand side is always a simple identifier in the cases used so far [but wait for extensions that may confuse this later on], I think for "c => expression" I would read "c 'lambda-function' expression"' or even "c 'arg' 'function' expression". In the last case, I could then say things like "b 'arg' c 'arg' 'function' expression".
It might be better to make it even more clear that a lambda-expression is being introduced and say something like "'arg' b 'arg' c 'function' expression".
Figuring out how to translate all of this to other languages is an exercise for the student [;<).
I still worry about "(b, c) => expression" and other variants that may come into being if they haven't already. Perhaps "'args' b, c 'function' expression".
After all of this musing, I notice that I am coming around to translating "c => e" as "'lambda' c 'function' e" and noticing that the mapping to exact form is to be understood by context: λc(e), c => e, f where f(c) = e, etc.
I expect that the "goes-to" explanation will prevail simply because this is where a dominant majority is going to see lambda expressions for the first time. That's a pity. A good compromise might be "c 'lambda-of' e"