Dear student,
Milk contains lactose which breaks down into glucose and galactose. Drinking milk has no relation with the accumulation of lactic acid in the body.
Lactic acid is a waste by product of anaerobic respiration and when excess accumulation occurs, your muscles "hurt" because it disrupts the normal pH of their environment. Luckily that excess lactic acid can be both used by the muscles in aerobic respiration and carried to the liver where it undergoes a series of chemical reactions (gluconeogenesis) to become an energy source for cell function throughout the body.
Regards