From the function name I think you need to find if there is any lowercase letter is present in the string. I don't solve home work problems but you are almost there, you made a small mistake.
Your function only checks for the first character as it has return statements in the else condition of the for loop.
print(any_lowercase1("cAmel"))
print(any_lowercase1("Camel"))
Remove the else statement and return False outside the loop like this,
def any_lowercase1(s):
for c in s:
if c.islower():
return True
return False
print(any_lowercase1("cAmel"))
print(any_lowercase1("Camel"))
print(any_lowercase1("CAMEL"))