What is the difference between cable 3x240 LV ??cable and 3x240MV or HV cable

Difference is for insulation rating. Insulation rating for HV cable is higher and hence more power transmission is possible.

and what the difference for construction design??

The term "medium voltage" (MV) is often used in electric power distribution and utilization. Electric power transmission is often considered to be high voltage only, but some definitions extend MV into the lower levels of power transmission voltage. For power distribution and utilization, LV would be about100V to600 or1000V. MV would be600 or1000V to anywhere between10,000 and100,000V. HV would be anything above MV except that the designations EHV and UHV may be applied to the higher ranges