Thread: How to install this lock?

Definitely make the box . Cut and fit the lid with its hinges and get it all flush . Then cut and fit the lock.
Its fitted based on working out the key position first. Get it center and the depth right , drill a hole the size of the key shaft and with that style of lock you could poke a cut nail through to locate the lock before doing some rough fitting . I usually tilt the lock back to view through the hole and make sure the keyhole stays over the drilled hole to creep up on the exact position while fitting at this stage . A couple of saw cuts and a sharp chisel and they are not hard to fit after that.

Then with the lock not yet screwed in the keyhole is further cut and enlarged.

Are you fitting an escutcheon ?
A bit of extra info not related to your question.

If you are fitting an escutcheon , fit the lock and get the point where the hole for the key goes through. Start with a small drill hole and then widen it out just so the key fits through and works the lock. So its not as big as the escutcheon hole . With the lock screwed in place and the key fitted so it works freely and doesn't touch any wood the key will drop a little . There's always a bit of wiggle in them. You then place the escutcheon hanging on the key shaft with the key in the lock . Position the escutcheon so its gap around the key shaft is even and then scribe around the escutcheon with a fine pointed sharp scribe and cut and fit it to that. by doing that the key sits perfect in its slightly dropped position and it looks perfect .

Then you lock the lock with its top pin plate fitted and bring the lid down to get a mark on the top to cut that in .

I agree with Auscab about making the box first, then cutting out the mortice for the lock. However, you can save yourself some time and effort if you mark out where the lock will go before assembling the box, and hog out some of the waste with a router. don't go all the way to the edge of where the lock will be, though. leave yourself a bit of wriggle room.
Depending on the size of the box, you will probably need a set of short chisels to cut the edges of the mortice, and you won't have much room to use the mallet. I use a set of Wood River chisels that are quite short and good quality.

If you know what size the box lid will be I cut the face board, use a Forstner bit & chisel to fit the lock then remove the lock cut a 1/16" strip of scrap wood or whatever the kerf of the cut was, glue the paned back up. this saves a lot of awkward chiseling. When you cut the lid the scrap wood disappears.