Dear all,
Finally I found solution how to run WIDI in Windows 8.1 with 60Hz frequency rate on TV.
You have to install Intel WIDI 3.5.40.0 application, which allows you to set 60Hz in 1080p resolution.
Enjoy ! 
MY CONFIGURATION:
Operating System - Windows 8.1
Tested TV's - LG 55 LE 8500
notebook - Samsung NP900X3C
- Intel® HD Graphics 4000
- Intel® Centrino® Advanced-N 6235
- Processor Intel® Core™ i7 3517U (1,9 GHz, L3 4 MB)