Below is a pic of the top handle/2.5" form factor drives 5.25" option made for the highest of the 3 possible optical drive bays in the Z420. That is made to slide forward to come out, not inwards. Note the two round black slider screws on that side.... there will also need to be two on the other side:
The thing you don't want when trying to remove it by sliding outwards..... no locking screw on either side. Note in the pic just beneath the arrow tip. You can screw in a locking screw through that little hole that prevents the unit from being slid forward out of the case. Beneath that little hole you can see 1 of the 2 slider screw heads. A locking screw on that side is easy to recognize as being in place. However if there is one on the other side then you need to take off that other cover to get access to it.
Most of the time there are no locking screws...... I bet you just need to work at it a bit, pushing outwards rather than inwards. It is easier to push forward if you take off the front cover first. Here's that second picture: