Contact the seller to ask what the battery output voltage is. It should be 6V. Anything less would impair the operation of your MiP. Given that it is being sold as a replacement unit to use instead of AAA batteries, it should be supplying the correct output. It never hurts to ask though.
The other thing to find out is the capacity in mAH of the LiPO battery.
Standard 1.5V AAA alkaline batteries can vary between 400mAH - 900mAH, depending on what capacity the manufacturer has decided to make. Their life span then depends on the load that they have to supply. Obviously the higher the battery load to less time they last. Also the more that they are used the less time they last.
Obviously if the LiPO battery has a greater capacity it will last longer. LiPOs also maintain their voltage well as they discharge so that should not be a problem.
This link may be of interest to you.