"When referring to a Lagrange Point, I'm referring to the most 'famous one':
L1, located at the gravitational balance point between Earth and Moon, nearly 200,000 miles away.
Why?
Why would NASA be interested in sending manned spacecraft there
at some future date [after ISS is 'completed']?

Granted! 200,000 miles from Earth is better than 200 miles, but what practical, scientific, or exploration-adventure justification could NASA provide for targeting Lagrange Points for manned missions? "

The "Near Earth space" has two L1's, the one between Earth and Moon isn't neccessarily "the famous one". For instance the Earth/Moon L-1 has never had a spacecraft visit it or even fly through it. Whereas the Earth/Sun L-1 has SOHO in it right now, and it is usually the L-1 that is commonly meant as L-1. I think people should call Earth/Moon L-1 the Near Point, since it's the nearest L-point in distance to Earth. (Note: a single planet like Venus or Mars has 5 Lagrange Points- in Earth's "binary system" we have 10 Lagrange Point [2 sets]).
Now, if you have studied using the Moon's resources to any great extent, then perhaps the Earth/Moon L-1 (and L4&5- the location for large space colonies made of Lunar material), then it might seem to you to be the "more famous" [it was the destination for mass driver's payload].

As to why NASA would want to send a manned spacecraft there, I'm not exactly sure. If you wanted to go to Mars with a crew, I would build/stage the vehicle at the "Near Point" . If you wanted a gas station, I would put it at the Near point. If you want something to "orbit" the Moon and have constant line of sight with the Nearside and uninterrupted communication with Earth and have nearly continous sunlight, I would put it at the Near point.