Python: for loop overwrites a lambda function created in the loop - python-2.7

Question

I'm working with Python 2.7 and I stumbled on this issue and I cannot even understand the logic of why the following doesn't work.
I need to fit different dataset and I want to do it dynamically in a for loop.
Here is a MWE that duplicates the problem:
import numpy as np
from scipy.optimize import curve_fit
def func_to_fit(x, a):
return x ** a
x = np.arange(0, 10)
dummy_dataset = {1: x ** 2,
2: x ** 3}
param = {}
fitted_func = {}
print "First loop"
for i in [1, 2]:
if i == 1:
idx = "Ex"
else:
idx = "Ez"
# store the results in different items in a dictionary to avoid the usual copying issues in Python
param[idx] = curve_fit(func_to_fit, x, dummy_dataset[i])[0]
fitted_func[idx] = lambda x: func_to_fit(x, *param[idx])
print idx, fitted_func[idx](x)
print param
print fitted_func
print "Ex", fitted_func["Ex"](x)
print "Ez", fitted_func["Ez"](x)
And the output is
First loop
Ex [ 0. 1. 4. 9. 16. 25. 36. 49. 64. 81.]
Ez [ 0. 1. 8. 27. 64. 125. 216. 343. 512. 729.]
{'Ex': array([ 2.]), 'Ez': array([ 3.])}
{'Ex': <function <lambda> at 0x0000000015989EB8>, 'Ez': <function <lambda> at 0x0000000015989F98>}
Ex [ 0. 1. 8. 27. 64. 125. 216. 343. 512. 729.]
Ez [ 0. 1. 8. 27. 64. 125. 216. 343. 512. 729.]
The behaviour before the print "Second loop" is as I expect: outside the loop where I do the fitting, the parameters stored in param are the correct ones ("Ex"=2 and "Ez"=3), the functions in fitted_func are stored in different memory locations, and when I call them in the first loop they give the correct results, namely fitted_func["Ex"](x) = x^2 and fitted_func["Ez"](x) = x^3.
However, if I call each fitted function individually, as I do with the last two lines of code, and I try to calculate the values of the functions, I have the wrong result, i.e. both functions return x^3.
I suppose this behaviour is somewhat connected to the way Python handles memory and with some kind of race condition, i.e., Python calculates every time the lambda function in fitted_func[idx] and remembers the last valid result (in this case, the fitting for x^3).
Anyway, I don't really understand what's the exact problem and how to overcome it.
Hoping I managed to illustrate the issue properly, does anybody have any idea of
1. What causes this issue?
2. How to overcome it?
Thanks a lot!