Yep, you need a triple.

One thing I'm not sure about is if you will find the LHT to be "fun" for non-touring rides. The geometry is designed for loaded touring, and it will be quite comfy for long rides, but for other uses you may find it a little sluggish.

You might want to check out the Bianchi Volpe and the Salsa Casseroll, as well as see if you can do a test ride on the LHT, before pulling the trigger.

If the LHT suits your riding style, I actually think you might do a little better with the stock / complete LHT. I have a slight preference for both Shimano and MTB components when it comes to touring bikes, because (as best I can tell) Shimano is a little more widely available, and MTB components are a bit more rugged. Plus, the stock is about $1000 USD.

And a minor tweak: look into the Nitto Noodle or Soba handlebars.