RE: Wire a LiPo into a Field Amp for Music?
"Timing the run" doesn't work so well with audio because current draw (and therefore runtime) varies tremendously with type of audio content (lots of bass vs little), overall volume, amount of clipping (distortion). Even though the input of that amp is rated 2A, don't be surprised to see average values around 1A, and peaks over 2A (again depending on content, volume, etc).
Personally that LVA (Low Voltage Alarm) would be the best bet to make sure you don't overdischarge the lipo - you just have to make sure you can hear it over the audio. You could mod the LVA and replace the speaker with a hi-brightness LED/resistor combo so you can see when the LVA activates. This would take a little experimenting.
As to the original question; yes, you can easily make an adapter that goes from Deans to whatever plug the amp uses. Just make sure you have the right polarity at the amp's plug! Incorrect polarity will surely blow the amp. The plug for that specific amp requires the tip to be positive (the "tip" is the inner hole and is +12, the outer sleeve is the ground). Use a voltmeter once you finish the adapter to make sure it's wired right.
Another thing to consider is the lipo voltage. Fresh charge on a 3s pack is 12.6v, and nominal is 11.1v, but some amps shut down below 10-11v.
One more thing; if you use this outside, you may need a bit more power. A house/room has walls to contain/reflect sound so it sounds louder. Outside, the same volume will not sound as loud and you may find yourself turning it up louder to compensate, and if you go too loud, the amp starts to clip which sounds horrible in these "digital" amps.