Just to illustrate what I think might be a problem (or two) …
First I assume you have the LilyPad “LEDs” wired in parallel (as shown below) and not in series. You don’t have enough voltage out of a single cell LiPo to make more than a single “LED” light up if wired in series … which kind of defeats the purpose.
As to whether you can run the sets of LP “LEDs” of a single LiPo and which is better, 500 mAH or 1000 mAH … I’ll say either should work and it’s a question of runtime. Obviously the bigger battery will last longer than the smaller one, though by how much is debatable.
What I expect is that as your “LEDs” do their dance, the blue and violet and white ones will get dimmer first. That’s because they need a higher voltage to run when compared to green and then yellow and then red LEDs. Your 3.7V LiPo really starts out at ~4.2V if fully charged and then drops, with use, down to 3.8V-3.9V fairly quickly. Over the majority of it’s runtime the voltage will then slowly drop to ~3.3V and then quickly drop to under 2.8V … if you let it. Don’t let it ! That can damage the cell. Different people pick different voltages to stop usage, anywhere from 3.3V - 2.8V. I doubt there’s actually that much difference in the runtime. So let’s pick 3V as the cutoff point to prevent battery damage. I expect you’ll not even get that far as I expect any blue/violet/white LEDs to be off, or to be so dim as to be worthless before the battery gets to 3V.
All LEDs need some minimum voltage across them before they will begin to flow current and illuminate. This voltage, in general, varies with the color of the LED. Reds need perhaps 1.8V, yellow perhaps 2V, green maybe 2.2V-2.4V and blues and whites need 3.0V-3.4V. And there’s more than that to it. The LP “LEDs” you linked to are actually an LED and a 100 ohm resistor in series with it. And then the conductive thread isn’t as good a conductor as normal wire. It adds a notable resistance, about 28 ohms/foot, to the circuit. And so you see these pictured in the the diagram below. Whenever current flows through a resistor, there’s a voltage created across it. And all the voltages for all these resistors and the LED must add up to equal whatever the battery voltage is at that time. Meaning the actual LED has less voltage across it than the battery voltage.
Typically circuits push perhaps 20 mA of current through a normal (not high power) LED to make it “bright”. Perhaps 5 - 10 mA will still be considered OK. Below that … it depends on your taste and the darkness of the room.
So let’s churn some approximate numbers. Let’s look at a red “LED” at short and long distances (thread length) from the battery and LP mainboard (MP3 board).
6" distance, red “LED” 20 mA requires 4.5V battery voltage. Ooops !
6" distance, red “LED” 5 mA requires 2.5V battery voltage.
16" distance, red “LED” 20 mA requires 5.4V battery voltage. Ooops !
16" distance, red “LED” 5 mA requires 2.7V battery voltage.
And for a white “LED” …
6" distance, white “LED” 20 mA requires 5.7V battery voltage. Ooops !
6" distance, white “LED” 5 mA requires 3.6V battery voltage.
16" distance, white “LED” 20 mA requires 6.7V battery voltage. Ooops !
16" distance, white “LED” 5 mA requires 3.9V battery voltage. Hmmm ??
So you can see you won’t be getting the max brightness that you could from the blue/violet/white “LEDs” using a single cell LiPo. Perhaps you’re OK with what you’ve got. Doubling up on the thread to those “LEDs” can help but it’s no cure. And that’s why there are [LP LEDs (no quotes) that don’t have the 100 ohms resistor included. You can also see how the decreasing voltage will reduce the current to all the “LEDs” and how the blue/violet/white “LEDs” will drop out first, perhaps even before you use most of the energy stored in the battery. So a 1000 mAH may not really buy you that much more runtime.
Lastly I should mention that a digital pin on a LP mainboard or MP board can only source or sink 40 mA max. Current in parallel circuits adds directly. So 10 mA through each of the “LEDs” in parallel means N*10 mA to be sourced or sunk by the LP pin (assuming no “driver” in between). In the case of the 3 “LEDs” shown, that’s 30 mA and while that might, just maybe, be OK, a better limit would be 20 mA into/out-of any pin. And that means you might drive 2 or 3 LP “LEDs” per pin … I think you had more than 2-3 in mind for any 1 set of “LEDs”.
http://dlnmh9ip6v2uc.cloudfront.net/dat … 3-v15a.pdf
https://www.sparkfun.com/products/11791
https://www.sparkfun.com/datasheets/Dev … ad-LED.pdf
https://www.sparkfun.com/datasheets/Dev … 50OVS4.pdf (red/yellow/green LEDs)
https://www.sparkfun.com/datasheets/Dev … 6QWF-D.pdf (white LED)
https://www.sparkfun.com/datasheets/Dev … ANB4-H.pdf (blue LED)](LilyPad LED Micro - White (5pcs) - DEV-10753 - SparkFun Electronics)