The "lifter rail" you referred to, I simply refer to it as a mounting rail, though I'm certain it has a "proper" name, has an 11mm dovetail which matches that machined into the receiver of your rifle. The top of the rail steps down to a 3/8" dovetail which is used by the scope mount. Some people like them, (I do) and some people prefer to have the mount attached directly to the receiver. If you decide to remove the rail, make sure you get a scope mount with an 11mm dovetail and rings which match the outer diameter of your scope...in this case, 1 inch..also ensure the mount includes a scope stop to help keep the mount from slipping. Almost everyone agrees a one-piece mount is the only way to go with a springer, especially the more powerful "magnum" springers. Leapers, out of Livonia, Michigan, sells scopes and mounts through many of the online retailers. If you check the Mall at the top of the page, it'll take you to many of the most popular. Leapers imports a Chinese scope with the Leapers name on it along with scope mounts to fit virtually any scope made. There are also "rebagged" Leapers scopes from Centerpoint and, if I'm not mistaken, UTG. Look in your mail inbox and you'll see what I mean. You can purchase a very nice Centerpoint scope from Walmart for around 70 bucks. I've got a couple of them...though one just died, they're easy to replace...just take it back to Walmart.
Dude, if you're getting 4" groups at 15 yards, you're doing about 2x as well as I did when I shot my first springer...I don't care how much coffer ya drink. Seriously though, just keep practicing. I've found the springers to be very hold sensitive (though the Diana isn't as bad as the Gamo's,) so it's simply going to be a matter of shooting them until you find the body position and hold your rifle prefers. Generally speaking, the more loosely you hold the rifle and the less pressure you exert on her, the happier she's gonna be.