Your musket was a Muster 1854 System Lorenz rifle musket. The Austrian Kaiser's double headed eagle on the lockplate ["bird"] is an Austrian Army [k.k. Army] acceptance - not inspection - stamp. K.K. Army weapons are liberally marked with assembly and inpection markings, but there is no known crib sheet for them. I don't see a k.k. Army unit mark on your limited photographs. The cheek piece on the left buttstock indicates that it was manufactured to k.k. Army standards, so I wouldn't necessarily be surprised if it was sold to the Federals or Confederates from k.k. Army war reserve stocks. The ramrod is not a k.k. Army ramrod. Cracking in the European red beech used in the stocks of these guns is common as the wood aged.
Since it is missing its sights, I can't tell if it was a Type I [block rear sight] or Type II [flip-up long range rear sight] variant. It was sold as surplus after the Civil War and transformed into a fowling piece [i.e., it was bored smooth, the sights were removed, and the rear sight slot was filled]. The saving grace was that the "sporterization" was fairly minimal, since often the stock and barrel were also shortened in transformation.
What to do with it? At this point it has no value to a knowledgeable collector as a Civil War or k.k. Army weapon, although it is worth more as parts than what you paid for it if you elected to part it out. You can clean it up, get a proper ramrod [good reproductions are available for less than $100], and hang it on the wall. Or, you can restore it as a shooter. I'm a shooter, so I would probably have the barrel relined to .58 caliber. Bobby Hoyt is one of the folks who does that type of work. He can also put a correct, although taller front sight on it, and I would see if he could remove the filler from the rear sight slot. Original Type I rear sights are available, as are good reproduction Type II rear sights.
Have fun with it.
Regards,
Don Dixon