So one of the auction tools I got is a Lyman 4 hole press. It was rusty and frozen but I got it all cleaned up and running. Since I can’t find a manual... can someone tell me ...

The upper screw holds the shell holder in. The bottom screw is only used when only priming empty cases? Only moves a short throw of the handle? Do I have that right? Also the shell holder is very tight/hard to get a casing in...file it or replace? And conversion bits?

You need one of these, that way you can use any modern shell holder you already have (Lee, RCBS etc)

Lyman Shellholder Adapter J-Type Shellholder Ram to - MPN: 7095762

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Straight shootin'
SWCA#2439

There is already an adapter in it. You may need to clean it up a bit with a needle file. Oh is the shellholder held in the adapter by a set screw? It may be threaded in a little. The bottom screw holds the priming posts for when you prime. If you have the originals they may be too short to prime with the shell holder adapter in place. Lyman has longer ones for use with the adapter.

I have one of those adapters for my Tru-Line Jr. press also, but I bought it off eBay for about $5. I think it is the same. You just slide regular RCBS-type shell holders into it. No set screws are required to lock the shell holders in place.

That looks like a regular J type shell holder in orginal posters picture, not an adapter.

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Straight shootin'
SWCA#2439

The shellholder is probably not allowing the proper head size brass case to slip into it because the left edge of the opening (as you look at the pic) is very slightly deformed.
You may have to enlarge the pic to see it or use a loupe if you have it in hand.
Looks like it was probably struck w/a hammer and peened that edge down a bit. The opening on the left side is not quite square and you can see the marks.

Carefully open just that left front side opening back up,,nothing else.
Might be a job for,,,,dare I say !!!,,,a Dremel with a very small disc and a steady hand.
Lacking that, a couple of needle files and a few minutes work will do it.

Looks like a nice sturdy press from what I can see in the pic.

Shell holders and priming punches are readily available on ebay. That shell holder looks a bit beat up so replacing it wouldn't be a bad idea. I have never liked the conversion kits to use standard shell holders. With the original Lyman parts so readily available it's not an issue to just buy the right parts. I have 10 of these presses set up to load, one for each caliber that I load for. they are an excellent press. The handle stroke should go from almost vertical to hitting the edge of your loading bench on the down stroke. If it doesn't then you may have something assembled wrong.

Lyman will send you an owners manual! I've been using an All-American press for 49 years!

Did you try this page on the Lyman site? It might have what you need.
Lyman User Manuals

If not ask Lyman for a manual like suggested above.

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Freedom is never free!!
SWCA #3437