When muscles lack oxygen this will start to build up and cause fatigue? ?

This happens because the muscle cells respire anaerobically and the glucose is not broken down completely, and Lactic acid is formed. The lactic acid causes pain in the muscles.

Oxygen is very important in cellular respiration, without oxygen only anaerobic respiration takes place and this results in two molecules of Adenosine Triphosphate (ATP) which is in basic terms energy. With oxygen 38 molecules of ATP is creating resulting in more energy. Another reason it's not good to not have oxygen present is the build up of Lactic Acid and this weighs the muscle down making it harder to move. 

Also understanding the Anaerobic (without oxygen) respiration formula and the Aerobic (with oxygen) formula is important in understanding fatigue of the muscle 

Anaerobic Formula 
C6H12O6 (Glucose) --> 2 Lactic Acids + 2ATP

Aerobic Formula 
C6H12O6 (Glucose) + 6 O2 --> 6 CO2 + 6 H2O + 38 ATP