How should I fix cracking wood around door lock?
You have an old wood door that used to have a Mortise lock in it.  Someone 'upgraded' it.
You have 2 choices:

stuff the cavity with whatever you can find, bondo, wood putty, etc.  Then buy a metal plate that &quot;wraps around&quot; the lock area.

Pull the lock out, pull out everything that smacks of wood filler.  Carefully measure the cavity and use a bandsaw, planer, jointer, etc. to take a piece of wood and shape it to slide into the cavity.  Make it just a bit wider and taller than the cavity so that it has to be tapped in with a hammer.  Then liberally smear it and the cavity with wood glue, tap it in, and clamp the door down tight in between 2x4's.  When everything has hardened redrill the doorknob holes.