A lock assembly comprising: a casing having a collar received therein, the collar located between an inner unity and an outer unit, the collar having at least one first slot defined axially in an inner periphery thereof; the inner unit having a first part, a first block and a first driving member, the first part driving the first block and the first driving member, the first block having a push portion, the first driving member having at least one first lateral piece that is located corresponding to the first slot, and a receiving hole that is located corresponding to the push portion, at least one inner spring located between the first block and the first driving member; the outer unit having a second part, a second block and a second driving member, the second part driving the second block and the second driving member, the second driving member having at least one second lateral piece that is located corresponding to the first slot, and at least one outer spring located between the second block and the second driving member characterized in that the second driving member has a contact portion that is located corresponding to the push portion and the at least one receiving hole; and when unlocking the lock assembly from outside of the lock assembly, the second block is moved toward the collar to compress the outer spring so as to axially push the first driving member to compress the at least one inner spring so that the first driving member is not located in the at least one slot, the second lateral piece of the second driving member enters into the at least one slot, the collar is operated by the second part via the second driving member; when unlocking the lock assembly from inside of the lock assembly, the first block is moved toward the collar to compress the inner spring, the push portion of the first block pushes the contact portion of the second driving member via the receiving hole so that the outer spring is compressed by the second driving member, the second driving member moves to a position where the second lateral piece is removed from the at least one first slot, the first driving member is pushed by the inner spring and the at least one first lateral piece enters into the at least one slot so that the collar is operated by the first part via the first driving member. a casing having a collar received therein, the collar located between an inner unity and an outer unit, the collar having at least one first slot defined axially in an inner periphery thereof; the inner unit having a first part, a first block and a first driving member, the first part driving the first block and the first driving member, the first block having a push portion, the first driving member having at least one first lateral piece that is located corresponding to the first slot, and a receiving hole that is located corresponding to the push portion, at least one inner spring located between the first block and the first driving member; the outer unit having a second part, a second block and a second driving member, the second part driving the second block and the second driving member, the second driving member having at least one second lateral piece that is located corresponding to the first slot, and at least one outer spring located between the second block and the second driving member when unlocking the lock assembly from outside of the lock assembly, the second block is moved toward the collar to compress the outer spring so as to axially push the first driving member to compress the at least one inner spring so that the first driving member is not located in the at least one slot, the second lateral piece of the second driving member enters into the at least one slot, the collar is operated by the second part via the second driving member; when unlocking the lock assembly from inside of the lock assembly, the first block is moved toward the collar to compress the inner spring, the push portion of the first block pushes the contact portion of the second driving member via the receiving hole so that the outer spring is compressed by the second driving member, the second driving member moves to a position where the second lateral piece is removed from the at least one first slot, the first driving member is pushed by the inner spring and the at least one first lateral piece enters into the at least one slot so that the collar is operated by the first part via the first driving member.