I have inherited several firearms from my Dad who was a serious shooter and collector from 1920 to his passing in the 1980's. My siblings and I each received some after my Mom loaded them all into her car and drove them to the East coast from their home in Arizona. The unmodded ones I can ID but this one has three separate gunshop employees stumped (all younger than me). 
I think it is started as a Model 1885 low wall Winchester and I would like your opinion on it. It has no visible serial number, only 22 Long Rifle and my dad's SSn stamped on the left side of the barrel. The barrel is 22 5/8" long, round, tapered to .645 at the muzzle. The action's tangs appear to be shortened (?), holes filled and modified for a stock thru bolt.
The scope is marked "M29S Special Scope, W R Weaver Co., El Paso, Texas".
I hope my pictures upload and thanks in advance for any help you can offer.

I agree with Waterman that the barrel is from an M1922 Springfield.  The general style of the rifle is that of the conversions to target or sporter/varmint rifles that were made in the '20's and '30's.

The action is a Winder Musket action, cut away for even easier loading of the .22LR cartridge.  The small Weaver 29-S scope was made between 1930 and the beginning of WWII.  Weaver made the first good affordable scopes in this country.  The mounts may be custom made--Stith mounts looked like them (especially the front mount) but were generally made to adapt to the sight slots and existing receiver holes of the rifles they were fitted to.  The holes in the receiver for the Winder peep sight were igonred and two new holes were drilled and tapped in the top of the receiver for the rear scope mount.  This one-mount-on-receiver, one-on-barrel was also very characteristic of between-the-wars work.

Somebody took a fair amount of trouble lightening the hammer, checkering the trigger and redoing the lever to that neat ball-and-curve to fit the pistol grip.  Clyde Baker has a picture of such a conversion in his gunsmithing book.  The lever and hammer look to be nickel plated without polishing, except where the shooter's hand has grasped the ball to open the action.  The stock is a pretty nicely done example of the modernized type, and good wood, too.  Is there anything marked on the inner surfaces of the wood or under the buttplate?

Short of something definitive like a maker's mark, it is a pretty good example of what a lot of gunsmiths of the period were doing during the single-shot rebuilding craze.  You might check with Michael Petrov.  He posts here rarely and also has a site of his own, doublegunbbs at doublegun or something like that.  He might have a better handle on whose hand turned your rifle out.

How does it shoot?

Now I've gotta take off the buttplate again. Should I get out the heat and lemon juice and check for invisible ink?

1937 to 1940 my dad was getting out of Tulsa University and looking for work on his way to Findlay, OH where he met my Mom.

I have a high wall that has the same action lever.  I was told by a collector that is is a Sedgley design.  Sedgley was a prominent gunsmith in the Philadelphia area in the 20's.  They made a lot of "wall" custom varminters and the lever was one of their trademarks.

This is the description from my father's inventory papers (which I did not have at the start of this thread):
"Winchester lever action single shot rifle .22 LR caliber. Low side wall with right wall lowered for easy loading. Pistol grip stock w/ fancy walnut w/ cheek piece. Lever inlet into pistol grip. Lever chrome plated. Weaver 330B scope 2 1/2 x mounted in custom non-adjustable mounts. Barrel is .22 cal from Springfield Sporter .22 cal target rifle."

He was an NRA Life member, joined in the '30s, worked for Remington both in Findlay, OH and Ilion, NY. I am posting pics of another Winchester from his collection that my younger brother has in a new thread .

Thanks to all for the help.