In terms of the fork, there would probably be few issues as long as you didn't go silly. A 100mm travel fork would probably be too tall but an 80mm fork probably wouldn't. Longer travel equates to more stress on the frame. Mountain bikes usually have more material... either as gussets or as more material in the tubes... around the head tube to accommodate the forces that a long travel fork can place on the frame. I doubt that the LHT is buttressed in the same way.

The real problem is going to be finding a worthwhile 80mm travel fork. You really want something that is more than a pogo stick. You want a fork that you can lock out when you don't want to use it.

There also might be a brake issue depending on what kind of brakes you want to use. Just getting a new quality fork with brake bosses for linear brakes can an issue. Getting a fork with bosses that can handle cantilever brakes really isn't possible anymore. You could always go to a hub mounted disc but you need to make sure the levers you use are compatible with the brakes, i.e. if you have cantilever brakes, you'll need a road disc while linear brakes will require a mountain disc.