Using a lambda function within another function

[buran]

I think your confusion is not with lambda, but with functions altogether. Let's look at your second snippet (fixed for the NameError) and with some additions from me

def foo(n,m):
    return lambda a: a * (n + m)
 
bar = foo(n=11, m=5)
 
print(bar(a=3))

on line#4 you supply values for n and m (i.e. arguments for foo() function, not the lambda. Now bar function is effectively the same as

def bar(a):
    return a * 16

and then you call bar(), supplying the a argument.

Now, what you describe as blueprint for function:

def my_power(power):
    return lambda x: x ** power
    
pow2 =  my_power(2) # pow2 will get an argument and will raise to power of 2
pow3 = my_power(3) # pow3 will get an argument and will raise to power of 3

print(pow2(2)) # x=2
print(pow3(5)) # x=5

Output:
4
125
>>>

Now there are other way to create "blueprints for function"

from functools import partial

def my_power(num, power):
    return num ** power
    
pow2 =  partial(my_power, power=2)
pow3 = partial(my_power, power=3)

print(pow2(2)) # num=2
print(pow3(5)) # num=5
# and you still can do
print(my_power(2, 3))

Output:
4
125
8
>>>