Your Tarmac and the LHT have different geometry. The LHT, like most touring frames, has a lower placed bottom bracket than the one on a road racing bike. The 60 and 62 you refer to are the respective length of each frame's seat tube from the center of the BB to top.

If the 60 tarmac fits you well, then I would tend to think you need the 62. I am in the exact same situation with a CAAD8 (Cannondale) and my LHT. To be sure make a comparison from top tube height to ground if you can.

Now, having said that, you should also compare top tube length, considering that you will want a more upright position on your LHT than on the Tarmac.

When you get your LHT, keep the fork tube at its full length, using spacers all the way. Test it, then reduce if necessary. Do not cut the steerer tube without trying the full length first and certainly not by comparison to your road bike. FYI: I kept the full length and like it this way.

For more info, go on the Google LHT group where there is plenty of information on fitting.