Hackers help: How to lock Pax sliding doors

lock

This is a question for those of you who own Pax wardrobes with sliding doors. I am wondering if attaching a lock like the one in the attached picture is feasible to prevent the doors from being opened. From the pictures, the doors look like they lie pretty close/tight against together which might prevent the metal tongue of the lock from sliding between them. Unless of course I were to chisel a “notch” out of the front door to provide room for the lock to slick through. Does this seem feasible?

Any other ideas on how to make lock the sliding pax doors? Ideally would like it to lock with a key.