I owned this same rifle some years ago..found on the Eastern Shore of Maryland. I spent some time researching the name Lydeck / Lyjack/Lydick/Littig finding very little positive evidence of its past history. All four of the mentioned names (likely to be one gunsmith spelled in a variety of ways) apparently made muskets in the Baltimore area - Ref: Hartzler-ARMS MAKERS OF MARYLAND. Not much more found, and of course it is possible the barrel is a replacement, albeit a good one.
I never found any reference for a Lyjack barrel maker, but the gun does not appear to be 18th century/Rev War period as Hartzler's Lydick listing... and I agree it looks a lot like a Virginia made rifle.
For what it is worth...
Patrick Hornberger