I have a TinyLily with a TinyLily battery adapter.  I have a 3.7v lipo battery from Adafruit.  When the battery adapter is disconnected from the tiny lily the voltage is 4.1 on the terminals of the battery adapter.  When the battery adapter is connected to the TinyLily the voltage drops to about .4 volts but the TinyLily does not start.

When powered from the USB connector the TinyLily works.  Do I need a higher voltage battery?

The Tiny Lili might have a short

-Make sure the battery has a good charge.
-Connect a small motor to the battery to see if the motor runs and if the voltage drops. (this will give you an idea if the battery is good)
-Use an ohm meter to measure the resistance of the Tiny Lili (measure from power to ground, with power disconnected). If the reading is close to 0 ohm's then that would mean that the Tiny Lili is shorted.

I use the hot air gun to resolder those chips, just make sure you secure the Tiny Lili so that it doesn't blow away.

Wel, it works from usmb connected to a computer, so I don't thing that the board is shorted.  The battery is fine.

I have the exact same problem, maybe even the same battery (3.7V, getting ~4.1V at terminals)

Is the problem that this isn't ENOUGH voltage?

I got it, thanks to a Google+ post that I stumbled across: The problem is that the positive/negative are reversed on the jst connector from the TinyLily battery adapter to how the battery is wired. If you do it just right, you can flip the power adapter over and put it on backwards (the power pins are over to one side, you can look at the traces on the board)

The clue was here: https://plus.google.com/104597932997273912838/posts/9MTfDnakmVv

I'm not really sure who has got it backwards here, but once you flip it over it works fine. Not exactly a secure connection though

Any thoughts as to why its wired this way?

Good pull alecf.  I flipped the connector wrong side over and slid it over until just the two power pins were used.  That got it working.