我记得离开家时,锁了门的.I remember ----- ----- ----- as I left home.

locking the door
remember to do sth.记得要做.(未发生)
remember doing sth.记得做.(回想...)
as I left home,当我离开家时,已经是过去,所以根据题意可判断为remember doing sth ..已经发生了.门已经被我锁好了!