Let's say you have 5 LEDs in parallel. You want a current of 15mA into each LED. 20-25 mA is the max current that you can give.
Let's say you choose a current limiting resistor such that total current = 5*15mA = 75mA
Now, due to different specifications/characteristics of the LEDs, let's say 2 of them burn.
Now you have 3 LEDs and a current of 75mA going. This could cause all 3 to burn out, either at once or one after the other.
When cells are in parallel, differences during charging and discharging cause the life time to decrease. However, with LEDs, you may damage the LEDs immediately.
Just use a current limiting resistor for each LED to limit current to each LED. So, when a LED gets damaged, it doesn't damage the others in a chain.
Hope this helps.
Tahmid.