Interesting that you should bring this up, as it is a hot topic in ALPA.
Everything that Neil said is true. In Canada the terminology is referred to as SIRO (Simultaneous Intersecting Runway Ops).
At the heart of the issue is that the FAA has approved LAHSO to AFM + 1,000 (aircraft flight manual) lading distances. In some cases, this isn't all encompassing enough, and goes against what the FAA and ALPA orginally agreed to.
Okay, so you are monitoring and know that LAHSO may be in effect. When arriving, you simply state your declination as follows: "Tower, Midstate 230 unable LAHSO". To ensure further adequate safety you may also state: "Midstate 230 cannot accept aircraft LAHSO on our runway." Expect a response.
On departing, you should make your intentions as clear as possible and as soon as possible. Do so when you switch up ground. "Ground, Midstate 230 request taxi to the active, unable to take off LAHSO".