1S Lipo Powered BLDC Motor Control?
A diagram and/or explanation of your proposed or available control signals and desired frequency of operation will help. 

A full H Bridge requires 2 FETs per leg or 4 per bridge.
 Each "leg" runs from V+ to ground with the motor connected to the middle.
 Each leg is switched to connect the motor lead high or low.
 Switching the motor led high and low simultaneously is very nearly always a very very nad idea :-).

A 1S LiPo cell produces 4.2V maximum output.
 The low side drive voltage for this is so easily provided for N Channel FETS that a large range of drivers would be possible.

If an N Channel FET is used for the high side it needs Vbattery + Vgate for gate drive. 10V of drive would usually be acceptable and as low as about 6.5V would work with FETs with appropriately low gate drive voltages.

As long as a source of say 10V can be provided at modest power levels for gate drive, the high side control is a relatively trivial operation. 

Bridge drivers are avaiable which provide high side gate voltages for hi-side N Channel FETs. Even many that would usually be used at much higher voltages are OK at 4.2V supply.

A LiPo cell can be run down to about 3V. As long as the driver IC ran OK on 3V it could be used directly.

A simple discrete design is possible. High side gate drivers can be as simple as 2 or 3 cheap small bipolar transistors per high side gate.



High side N Channel drive is not overly hard, but use of P Channel high side FETs means a high side driver supply above Vbattery is not required and high side drive becomes very very very easy indeed. If I was doing this at 6A and 4V or so then I'd see if suitable P Channel FETs were available (cost, specs, ...) as overall the circuit becomes very simple.