Because some New York lines have four tracks (for fast/slow trains) of
which one pair can be used for all services at night. So theoretically
engineering on Finchley Road - Wembley Park or Barons Court - Acton Town
needn't close the line (although I'm sure the HSE would disagree).

You'll find only the 4 track lines continue to run 7 days a week, 24 hours a
day. The lines with only 2 tracks are shut at times for engineering works
and bus replacement services are offered. Aren't the 4 track lines more
separated than LUL / NR in most places, thus not having the engineering
staff subject to be hit by moving trains?

No, they are all scheduled to run 24/7:
http://www.mta.nyc.ny.us/nyct/service/schemain.htm

There is no regular downtime planned into the schedules, even for 2
track lines, like the L, the Manhattan part of the 7, the M North of
Broadway/Myrtle, or the J/Z in Queens. If you'd got the impression
that 2 track lines are closed a lot, it would be because the L train
is currently being upgraded to use CBTC. Of course it does happen that
the 2 track sections tend to get closed. A Passenger Service Advisory
is then posted - this certainly doesn't happen every night or indeed
every weekend.

Of course there are also a lot of 3-track sections (mostly Els, but
also the Concourse Line), the middle track of which can be used for
peak direction express (like on the 6 in the Bronx or the 7 in Queens)
as well as providing a way of keeping service running whilst MOW are
on the tracks. The only one which really doesn't get much use is the
West End express track (D train in Brooklyn) - the trains tend to be
sent over the Sea Beach (N) Line in one direction.

As far as separation between tracks goes, it's very variable. There
are sections with curtain walls, others with columns. There are of
course areas with lots of clearance and others with very little.