Anything North (which is really east) on NYC is MNRR not LIRR. Anything East of NYC on Long Island is LIRR but has nothing to do with Amtrak.
Contrary to the impression you are giving, Amtrak and LIRR actually share tracks east of Penn Station through the East River Tunnels upto the east end of Harold interlocking, and all that is on Long Island, albeit in the borough of Queens.
Indeed, Jis. Additionally, AFS1970 is overlooking the Amtrak owned Hell Gate Line that runs between Harold (jct with LIRR) and CP216 (Jct with MNRR) which is designated east/west by timetable.
The NEC thru NYP Is an "East-West" railroad, by timetable designation. Even if you head north on the Empire line, that is designated westbound by timetable direction,,,
The NEC is east/west from Boston to Zoo interlocking just outside of Philadelphia. At Zoo, the Harrisburg Line continues east/west while the PW line to Washington is designated North/South.
The designation from "A" interlocking in New York to Hoffmans (almost 10 miles past Schenectady) is north/south. This includes the former Empire Connection and MNRR's Hudson Line. The designation becomes east/west after Hoffmans and if you're on the Post Road branch (jct just outside of Albany.)
Just for giggles, Amtrak's former Atlantic City line (which is leased to NJT) is designated north/south between Shore Interlocking and Atlantic City.