LAG works for a fixed number of rows before the current row.

For all the rows prior to the current row, wouldn't you use something like ROWS BETWEEN UNBOUNDED PRECEDING AND CURRENT ROW in the OVER clause?

https://www.simple-talk.com/sql/learn-sql-server/window-functions-in-sql-server-part-2-the-frame/

http://sqlmag.com/sql-server-2012/how-use-microsoft-sql-server-2012s-window-functions-part-1

https://www.simple-talk.com/sql/t-sql-programming/sql-server-2012-window-function-basics/