u have to use npn transistor to power your leds i don t thinks lily pad can handle 5 leds per pin, read this post http://lanavajadelgeek.blogspot.com.ar/2011/07/aprende-como-funciona-un-interruptor.html use google traslator
to traslate all the page
realy is very easy in general a transistor (npn) have 3 leg base, emiter, colector
base: is the pin that recive the signal from the arduino (micro, ect) and let pass voltage from colector to emiter
emiter: conected to comond ground
colector: conected to the ground of the led
and the code u can use raw code, a variable "state"
if (state == 3) {
     state = 0;
          }
if (button1 == HIGH){
     state++;
              }
if (state == 0) {do something1;}
if (state == 1) {do something2;}
if (state == 2) {do something3;}
if (state == 3) {do something4;}
this is an idea no the actual code you have to add the timer to the button to lock him from been trigger alot of times in 1 push