There has been much debate about whether or not a woman can breastfeed her baby and continue to exercise due to the lactic acid build-up in her system. After doing some research and talking to highly tuned athletes who have had children, my conclusion is that it is perfectly safe and okay to exercise while you are breastfeeding.
To understand how lactic acid could alter the taste and/or effectiveness of breastfeeding, you have to understand how you reach the level of lactic acid build-up in the first place. Regular, moderate exercise will not cause lactic acid to build up in your system. It is only when you reach your anaerobic threshold that you begin to produce lactic acid and it enters into your system. Unless exercise intensity is very high (above the aerobic threshold), there is little change in lactate levels in either maternal blood or breast milk (Dr. James Clapp, Exercising Through Your Pregnancy).
Healthy, breastfeeding women may continue to exercise if they wish and it will not interfere with either the quantity or quality of breast milk. Even if you partake in frequent interval training at an intensity that exceeds your anaerobic threshold, this may only altar the taste and decrease infant receptivity due to an increase in lactic acid levels in the milk. Again, this will cause no harm to the baby and will disappear in an hour or two.