You don’t need to iterate the array. Just:
>>> x = ['ala@ala.com', 'bala@bala.com']
>>> x
['ala@ala.com', 'bala@bala.com']
>>> x.remove('ala@ala.com')
>>> x
['bala@bala.com']
This will remove the first occurence that matches the string.
EDIT: After your edit, you still don’t need to iterate over. Just do:
index = initial_list.index(item1)
del initial_list[index]
del other_list[index]