You have got to be kidding me!
The LHC has a circumference of 17 miles. It has no need to take the curvature of the earth into account because it is so small compared to the actual size of the earth. (See the magic of perspective). The earth's circumference at the equator is, for example, is 24901.55 miles. The ILC, on the other hand, will have a circumference of 31 km, which makes it slightly less than twice the size of the large hadron collider. Therefore, since it is larger, this one does indeed need to take the curvature of the earth into account. I present for you here this abstract from the scientific research paper presented by the good folks at CERN.
"In the base line configuration, the tunnel of the ILC
will follow the earth curvature. The emittance growth in
a curved main linac has been studied including static and
dynamic imperfections. These include effects due to current
ripples in the power supplies of the steering coils and
the impact of the beam position monitors scale errors" (Eliasson, et. al, 2006).
Eliasson, P., Latina, A., Schulte, D., Poirier, F., & Walker, N. (2006). Study of an ilc main linac that follows the earth curvature. In Proceedings of EPAC Edinburgh, Scotland: Retrieved from
http://accelconf.web.cern.ch/accelconf/e06/PAPERS/MOPLS098.PDF