I have seen LHTs come with the Conti TourRide tires and with Conti Contact tires. My friend's LHT came with Conti Contact tires, which I like better than the TourRide tires. I have one bike in my stable with TourRide tires and one with Contact tires. If you plan to spend a fair amount of time on gravel, the TourRide tires feel a little more sure footed. Otherwise, I don't like how the tread handles in turns, especially when wet. The newer Conti Contact tires have a better suited tread for street riding.
My personal choice for a touring tire is the Vittoria Randonneur Pro. The ride and grip in corners are better in y usage than on both Conti tires mentioned above, and they have served me well as far as puncture resistance is concerned. I have pulled out many goathead thorns from the tread, and not one has punctured the tube. (I hope the bike doesn't hear me, as I'm sure to doom myself to a flat on my next commute.)