First, the discharge current should not be too large, too large current will cause the battery internal heat, may cause permanent damage. On mobile phones, this is not a problem, can not consider. The larger the battery discharge current, the smaller the discharge capacity and the faster the voltage drops.
Second, never over discharge! The internal storage of electric energy in lithium batteries is achieved by electrochemical reversible chemical changes, excessive discharge will lead to irreversible reaction of this chemical change, so lithium batteries are most afraid of discharge, once the discharge voltage is lower than 2.7V, it may lead to battery scrap. The good news is that cell phone batteries are already equipped with protection circuits that will kick in and stop discharging before the voltage is low enough to damage the battery.