I am making a circuit which is powered by a lipo battery of 11.1V(3.7V*3). I need to check for the lipo's under-voltage so that the circuit automatically switches to a second lipo when the first one drops below the cutoff voltage. I am open to using arduino and relays but no diodes(as they lead to large power loss).
The problem you are facing has a solution. It is called "Power Path Controllers". Please examine the following portfolio of Linear Technology (now Analog Devices) products, Power Path Controllers and Ideal Diodes, I am certain some ICs will fit your need.
It looks like this one might work for you, LTC4419.