PostgreSQL: Calculate balance working backwards from current balance
You need a Window Function indeed. However LAG is not the right one. SUM(...) OVER(...) is the one you want. See SQL Fiddle.

Query:

SELECT account_id, activity_date, amount
    , SUM(amount) OVER(PARTITION BY account_id ORDER BY activity_date) as balance
FROM transfers t
ORDER BY account_id, activity_date DESC;


Output:

account_id  | activity_date                 | amount    | balance
1           | 2015-12-24 20:27:00.6700000   | 10        | 180
1           | 2015-12-19 12:13:50.0850000   | -275      | 170
1           | 2015-12-18 23:56:22.5130000   | 10        | 445
1           | 2015-12-18 23:54:46.8800000   | 50        | 435
1           | 2015-12-17 03:32:10.7070000   | -120      | 385
1           | 2015-12-12 03:56:50.7750000   | 35        | 505
1           | 2015-12-11 23:09:40.2110000   | -20       | 470
1           | 2015-12-03 01:17:59.4600000   | -10       | 490
1           | 2015-11-23 15:39:35.0030000   | 500       | 500