S Note is tightly integrated with Samsung's framework and thus can't be ported to non-stock-based ROMs.
In the meantime, try Squid as an alternative. Lots of available pre-defined notes, export to PDF, and best of all it makes use of the spare button on the pen that LineageOS doesn't use.
I have seen a similar issue trying to sync S Note's between a Galaxy Note 3 (smartphone) and a Galaxy Note 10.1 (as well as to a Galaxy Note 2).
The issue seems to be in the version of S Note running on Android 4.3.
On my Note 3, S Note saves the files as .spd files in a Snotedata folder. On the Galaxy 10.1 the S Note documents are as .snb files in the "S ...
As far as I know it is (still) not possible. You can now "zoom" the canvas which might suit your purposes. The original physical extents of the canvas remain.
As an alternative, I highly recommend Squid (formerly named "Papyrus". I have looked for apps specifically for an "infinite" canvas and find Squid quite suitable.
My only beef with Squid is that ...