Is it possible to use a lead-acid battery as a power bank?
You should use a low dropout voltage (LDO) regulator, which is a type of linear voltage regulator, to reduce your battery voltage (which could vary from about 5.6V when empty to about 7.2V when charging) to the 5V required by your phone.

There are many to choose from; LT1529 is a good choice since it comes in a TO-220 package, is stable with a single 22 uF output capacitor, and has a version with a fixed 5V output rather than needing two resistors to set the output voltage.  You can buy one, and the necessary output capacitor, on Digikey.

You may need to do something with the USB data pins (connect a 200 ohm resistor between them, short them together, tie them to ground or +5V, or make an intermediate voltage with a potential divider) to make the cellphone charge at full rate.  Google should tell you what it needs to be for your particular cellphone; the first method I mentioned is the official USB standard but not all cellphones support it yet.