My deerstalker has three screws in the tang. The spacing measures up between the center screw and the lower tang screw for my TC peep sight. The hole spacing on the peep sight is 1-1/4". If I had to tap, the instructions with the TC sight says to use a #29 drill and 8-32 thread tap.

Looking on Lyman's website, they show a Lyman 57 SML and a 57 GPR sight. And they say that the GPR sight comes with an adaptor. See mounting instructions for the 57 GPR in the quote box below. I found the instructions on a thread on thehighroad at this link: Tang Sight for GPR - Thread from thehighroad.org, 3rd post

Just looking at your pics of the GPR and my Deerstalker, it looks as though the drop rate of your tang may be a little more. If so, that tapered adapter block described in the instructions probably compensates for it. I.E., perhaps a tapered shim would be required for the TC peep sight? Note in the instructions the centered tang hole present in GPR's manufactured after April 1997. My Deerstalker has a center hole and the spacing fits. I wonder if that adaptor block could be ordered directly from Lyman sans the 57 GPR sight?

Quote
INSTALLATION OF 57GPR ON LYMAN GREAT PLAINS RIFLE

The Lyman Great Plains Rifle (made before April 1997) will require one hole to be
drilled and tapped for the enclosed 8/32 screw. Rifles made after April 1997 will
have the hole drilled and tapped at the factory.

1. Remove slide from sight base.
2. Unscrew and remove rear tang screw. The original rear tang will not be used.
3. Place enclosed sight adapter block on tang (still in stock) so that the thick end of
the adapter block is at the rear of the tang and the angled front edge lines up with
the angled front edge of the sight base.
4. Place sight base on adapter block and attach it using the wood screw supplied
with the adapter block. The screw is positioned in the rear hole and will pass
through the sight base, adapter block and rifles tang, and then is screwed into the
stock.
5. *Mark center of front hole on the tang and drill with a No. 29 drill (removing the
tang and clamping it in the vise will protect the stock of the rifle during the drilling
operation).
6. *Tap hole for 8/32 thread.
7. Secure sight base and adapter block to the tang with wood screw and the 8/32 x
1/2" machine screw that is supplied with the adapter block.
8. Replace with slide.
Installation is complete


In the 4th post of that same thread, mykeal shows a GPR with a different tang sight. Pics linked below of that:

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