Have you tried different HDMI cable by any chance?
Are you using any adapters or are you using straight connection from the laptop to the monitor?
If you are using some kind of adapter for any reason try to use straight connection to see the results.
Also, you can try to access the Intel® HD Graphics Control and see if both monitors are detected there the one for the laptop and the external monitor.
Once you open the Intel® HD Graphics Control try to low the resolution and the Hz and see if that works for you.
Hope that can help
Thank you Ivan,
I'm using a direct connection, there is no adapters in between. Tomorrow I will use another device in order to test the cable (It is new).
I tried to use Intel HD Graphics Control (changing resolution and frequency), unfortunately there is no other monitor detected but the laptop one.
I will try also to shave the plastic surrounding the jack since some Lenovo Yoga 2 users report contact problems. This way I will exclude all the hardware component.
Thank you again
I'm rather embarrassed, but I have discovered that all the problems are due to the cable connector. Finally my laptop has not problem to menage two monitors.
Anyway thank you for the assistance and I want to apologize for the wrong question.