The display was easy enough to removed from the stand, but there were no other apparent screws to open the plastic shell. I checked under the rubber bumpers at the bottom where such is often hiddent, but there were none there. I ran my fingernails across the label sticker on the back another common place to hide them. I did find one depression near the middle. Though not optimistic, I cut through the label with a knife, to find what I kinda expected, it was just a plastic molding depression.

I was going to proceed with the usual flat blade prying between the plastic halves along the edge, but before doing so, a quick google search for "LA2405x disassembly" resulted in this document from the manufacturer:
http://h22235.www2.hp.com/hpinfo/globalcitizenship/environment/productdata/Countries/_MultiCountry/disassembly_monito_2012417235645.pdf

It is a disassembly guide for recycling companies to know how to remove parts for recycling. It doesn't show all the key steps in detail, and it uses slightly destructive means, but the pictures did help. I could identify in them that the front and back plastic were indeed just attached with tabs and hooks as is common on such plastic assemblies.

Prying around, I was able to slowly get the plastic tabs apart. This freed the internal assembly which was not attached to the plastic at all, except for the wire leading to the front panel controls. Both the front and back plastic came off at that.
Disassembled, I could clearly see the LVDS data cable going to the panel, and a separate cable going to the backlight. As this backlight powers up, I wanted to stop here in my disassembly to make some measurements in order to determine how to drive the LEDs.