There is a non-trivial ammount of users that try to parenthesize lambda parameters:

>>> lambda (x,y,z): x+y+z
  File "<stdin>", line 1
    lambda (x,y,z): x+y+z
           ^
SyntaxError: invalid syntax

We should improve the error message in this case

Example:

>>> lambda (x,y,z): x+y+z
  File "<stdin>", line 1
    lambda (x,y,z): x+y+z
           ^^^^^^^
SyntaxError: Function parameters cannot be parenthesized

Why not "lambda parameters cannot be parenthesized" (optionally "lambda function")? def-ed function parameters are parenthesized, so just saying "Function parameters cannot be parenthesized" seems very weird.

> so just saying "Function parameters cannot be parenthesized" seems very weird.

I agree that the wording can be improved, but is not weird, it has the same problem in functions:

>>> def foo(x,y,(z,w),k):
  File "<stdin>", line 1
    def foo(x,y,(z,w),k):
                ^
SyntaxError: invalid syntax

With PR 28906 it will show:

>>> def foo(x,y,(z,w),k):
  File "<stdin>", line 1
    def foo(x,y,(z,w),k):
                ^^^^^
SyntaxError: Function parameters cannot be parenthesized

I am happy to take suggestions for the wording

+1 on adding better error messages for these cases. I also agree with having different explanations with lambda and def.

Below is what I have with friendly-traceback: perhaps the first line of both of these might be suitable?   (I will likely change the first line in each case to be as similar to what you end up with.)

>>> set_include("why")
>>> lambda (x, y): x + y

    `lambda` does not allow parentheses around its arguments.
    This was allowed in Python 2 but it not allowed in Python 3.

>>> def foo(x, (y, z), w):

    You cannot have explicit tuples as function arguments.
    You can only use identifiers (variable names) as function arguments.
    Assign any tuple to a parameter and unpack it
    within the body of the function.

I suggest "Lambda expression parameters ...".  Keep "Function parameters ..." for the other.

Note that the first error is adding invalid outer parens, whereas the second is adding inner parens for sublist.

> Note that the first error is adding invalid outer parens, whereas the second is adding inner parens for sublist.

Yeah, but you can also write:

lambda x, (y, z), w:  None

So is kind of the same error

New changeset 7a1d9325287a39528b795b1e8037146777abfe3e by Pablo Galindo Salgado in branch 'main':
bpo-45450: Improve syntax error for parenthesized arguments (GH-28906)
https://github.com/python/cpython/commit/7a1d9325287a39528b795b1e8037146777abfe3e