If it's lathe and plaster (and you do need to know) then it proably won't be on timber battens. It was normally fixed to the wall with lumps of 'cement'. L and p has no strength at all to carry a load of even 2 Kg and def not 9.
Your problems are worsened by the pre drilled holes in your cleats.
If I were doing this I would mark on the wall where the holes for the screws in the cleats will be, and then attach horizontal wooden battens to the front of the lathe and p and attach the cleats to those. This will move the whole thing out by an inch, but you can secure these battens really well by first drilling through the L & P with a 1" hole cutter for each screw needed so you can easily tap in a wall plug. An inch hole will let you see to locate the batten screws into the plugs. They screws need to be in the wall, if the brick is sound, about 40 mm. 3 screws per batten should do, or 4 if the battens will be more than 75mm wide. The point of wall marking your cleat holes is ofc to establish the position of each row of cleat screw holes to get the battens lined up ready, and (obvs i know) to make sure you place the batten screws away from the where the cleat screws will eventually go.
Don't over tighten the batten screws, but just a firm fit against the L& P. The battens in place will cover your 1" cut holes. slap a bit of wall paint over them if their ends will be visible.
It's now an easy job to fit your cleats with whatever screw will just go through the whole depth of the batten. A normal woodscrew will do fine.