Where Is Lactic Acid Produced?
Lactate is actually a product of cellular metabolism and is produced in various cells throughout the body including muscles, brain cells and red blood cells. Lactate and lactic acid are actually used as a fuel by some tissues in the body including neurons and cardiac (heart) muscle.

Skeletal muscle cells that produce lactic acid
Credits Lactic Acid
The fact is there is so much more to lactate than its supposed role in acidifying the cellular contents of muscle (a myth that can easily be deconstructed) and it is integral to our existence. There are a few paths that lead to the production of lactate from different substrates, but the most important pathway in exercise is the by glycolysis from glucose or glycogen.
Do liver cells produce lactic acid?