Why don't we use mobile phone in the lift ?

To put the answer in the right prspective, mobile phones communicate using electromagnetic (EM) waves of frequency from 900 MHz to 2100 MHz. EM waves travel by mutual interaction of electric and magnetic fields. Thus the wave does not need any medium for propagation.

Since metals are conductive to electric fields, when the EM wave passes through metals, the electric field of the wave causes electrons in the metal to flow. As such, energy is deprived off from the EM wave, the wave therefore loses its energy and weaken.

Lift cars are usually made of metallic substances, this is why EM wave from mobile phones becomes weaken when communication is made inside lifts.

Moreover, the lift shaft is a long tube of dense concrete. The attenuation of the concrete to the EM wave further reduces the wave intensity, thus making communicaton even more difficult.