What is the average current drawn by this motor https://www.pololu.com/product/2827. Can i use a lithium ion battery pack which provides 1- 2A current to run this motor.
The average current depends on the load and the voltage. At 12V the current will be between 0.3 (no load) and 5 Amperes (stall).
If your lithium battery can’t supply the current required by the load, the motor will run slowly and not deliver full power, and the battery pack could possibly be damaged.