TypeError: list indices must be integers or slices, not str

First, array_length should be an integer and not a string:

array_length = len(array_dates)

Second, your for loop should be constructed using range:

for i in range(array_length):  # Use `xrange` for python 2.

Third, i will increment automatically, so delete the following line:

i += 1

---

Note, one could also just zip the two lists given that they have the same length:

import csv

dates = ['2020-01-01', '2020-01-02', '2020-01-03']
urls = ['www.abc.com', 'www.cnn.com', 'www.nbc.com']

csv_file_patch = '/path/to/filename.csv'

with open(csv_file_patch, 'w') as fout:
    csv_file = csv.writer(fout, delimiter=';', lineterminator='\n')
    result_array = zip(dates, urls)
    csv_file.writerows(result_array)