Even the lambda expression when running on the computer, is acting out a Turing machine; head travels over symbols on a tape, reads a symbol, changes state, stops or moves...

that is what I meant by old wine in new bottles.

You're correct, unless your hardware is specifically designed for lambda calculus (like one of those old lisp machines), lambda code gets compiled into Turing instructions.

But why code in a Turing style (whether it's Java or assembly) when lambda programming is more efficient?

That's the point all the lambda folks are making.

"unless your hardware is specifically designed for lambda calculus (like one of those old lisp machines)"

No, I am talking about - at a deeper level, all computing can be reduced to a Turing machine. (Unless you are reading Roger Penrose on consciousness).

Maybe I am mistaken, I am out of touch.

to clarify:

A Turing machine can simulate a deterministic finite automaton and a non-deterministic finite automaton.

All systems are arguably either of these two. Perhaps that's why we can simulate weather, and lots of other things.

Unless you look at human consciousness - Nobelist Roger Penrose has a theory that the mind is not a computer. That it has quantum states. (his book: The Emperor's New Mind - I didnt finish it - long and hard).