You can give a key to tell list.sort or sorted how to sort.
A key to sort by the first value is lambda x: x[0]; a key to sort by the second value is lambda x: x[1].
d = {'user_0': [['item_805696', '2021-02-11 13:03:42'],
                ['item_849824', '2021-02-11 13:05:04'],
                ['item_386903', '2021-02-11 13:03:52'],
                ['item_3832',   '2021-02-11 13:04:07']],
     'user_1': [['item_58840',  '2021-02-11 13:16:11'],
                ['item_947129', '2021-02-11 13:15:27'],
                ['item_97057',  '2021-02-11 13:03:42'],
                ['item_640213', '2021-02-11 13:17:40'],
                ['item_644971', '2021-02-11 13:09:32']]}
for v in d.values():
    v.sort(key=lambda x: x[1])
print(d)
# {'user_0': [['item_805696', '2021-02-11 13:03:42'],
#             ['item_386903', '2021-02-11 13:03:52'],
#             ['item_3832',   '2021-02-11 13:04:07'],
#             ['item_849824', '2021-02-11 13:05:04']],
#  'user_1': [['item_97057',  '2021-02-11 13:03:42'],
#             ['item_644971', '2021-02-11 13:09:32'],
#             ['item_947129', '2021-02-11 13:15:27'],
#             ['item_58840',  '2021-02-11 13:16:11'],
#             ['item_640213', '2021-02-11 13:17:40']]}
Note that this only works because the timestamps are presented in the very practical format 'yyyy-mm-dd HH:MM:SS', and strings are sorted lexicographically, i.e., from left to right. If the timestamps had been in a less friendly format, such as 'dd-mm-yyyy HH:MM:SS', then you'd need to use the key to parse the timestamps.