PostgreSQLウィンドウ関数はNULL値を無視します

私はあなたがただすることはできないと思います：

select
from tbl_x
window w as (partition by ID order by Date)
where col_a is null;

そうでない場合は、次のことを行う必要があります。

select
Col_A,
Col_B,
case when Col_A is null
  then (select col_a
          from tbl_x x2
         where x2.id = x1.id
           and col_a is not null
           and x2.date < x1.date
      order by date desc
         limit 1)
  else Col_A
  end Col_A_Lag,
case when Col_B is null
  then (select col_b
          from tbl_x x2
         where x2.id = x1.id
           and col_b is not null
           and x2.date < x1.date
      order by date desc
         limit 1)
  else Col_B
  end Col_B_Lag
from tbl_x x1;

適切なインデックスを作成すれば、パフォーマンスはおそらくかなり良いでしょう。

create index ... (id, date desc, col_b) where col_b is not null;