Lactic acid builds up when the muscle cells do not have enough oxygen and begin creating energy without oxygen. This new (anaerobic) process produces lactic acid as a byproduct.
In order to keep this from happening your goal should be to get as much oxygen as possible to your muscles.
What are some ways to do this?
This works for two reasons. If you stick with it, breathing through your nose will act as a governor keeping you from the intensity that would convert you to anaerobic energy production. The second reason is it will increase your CO2 tolerance. With higher tolerance to CO2 you will be able to continue using aerobic (with oxygen) means of energy production for a longer amount of time.
Though at first this causes you to release more lactic acid (you aren’t getting any oxygen when holding your breath) you are training yourself to acclimate and adjust to this environment. This is similar to how you feel less lactic acid the 20th time you do a workout than you do the first time. Your body has adjusted. Breath holds drastically cut down the time it takes to acclimate though. Using breath holds will help you to produce more red blood cells and become more tolerant to CO2, both of which will cut down on the production of lactic acid in the future.
Unlike the first two methods, which are long term adaptions, save this short term solution for competition or testing events. In the long term you want your body to adapt and become used to higher levels of lactic acid. However, if you want to avoid the build up of lactic acid at all costs immediately you can do so by concentrating on breathing more than you normally would. Bringing in enough oxygen will ensure your muscles are getting as much as possible, keeping them from creating lactic acid. At the same time, by exhaling well, you will off load much more CO2 with each breath. This will help reduce the overall acidity of your blood and reduce the “burning” sensation in the muscles.