How does a departure off a runway used for LAHSO operations work?
The LAHSO line and pulsating white light bar applies only to landing traffic (when in effect and when accepted).

A phraseology example is:


  ATC: "(Aircraft ID) cleared to land runway six right, hold short of taxiway bravo for crossing traffic (type aircraft)."


There is no phraseology equivalent to a departing plane that has to do with LAHSO operations. If a runway is shortened for any reason, "shortened" will be added to the taxi and takeoff clearances, but this is another matter.



When a departure is involved as shown above, it is the landing traffic that needs to land and hold short.



Image source, reference, and further reading: AIM