2004 Buick Lesabre trim removal

It should come down as a unit, not as a cover. Here is the procedure, try pulling down at front first. A note of caution, some retainers are stronger than what they retain, and it is possible that breakage may occur. While this is not necessarily specific with your situation, it is a general rule of thumb on trim work. Here is the procedure.

Roof Console Replacement
Removal Procedure

Important: Do not let the overhead console hang from the wire harness.

Carefully pull down on the overhead console in order to release the retainer clips.
Disconnect the wire electrical connector.
Remove the overhead console.
Installation Procedure

Connect the wire harness.
Install the overhead console into the opening in the headliner.
Push in on the overhead console in order to engage the retainer clips.