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I suspect ypur problem is lack of current (amps) rather than voltage. You don't say what is the capacity of your 11.1v LiPo?
You need to draw a diagram showing how things are connected and post a photo of the drawing.
The servo should NOT be drawing power through the Arduino.
LiPo cells don't provide a convenient voltage for a servo. 3.7v is low and 7.4v is too high. A pack of 4 or 5 AA NiMh cells would be ideal.
You could, perhaps, power the servos from your 11.1v LiPo using a 7805 voltage regulator to drop the voltage to 5v.
...R
Plan your power system carefully - separate out the high power/current items
completely from the digital logic and sensors - saparate power systems is most
reliable, or you may get away with deriving the logic supply via a switching regulator
with a tolerant range of input voltages.
If you motors take the most power, use battery pack with the right voltage for them
as primary power. If servos dominate, 6V battery is obviously the right thing to do.
If your receiver needs 12V, perhaps you can derive this via a boost converter from
your logic supply?
Inevitably some sort of compromise usually has to be made, the real world is messy...
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A boost converter is a converter that boosts voltage. See also buck converter.
A logic supply is the supply for logic chips that require a clean spike-free
voltage for undamaged operation.
Wikipedia, Google...