If those peaks are correlations between J-coupled protons, then such shape is likely caused by the coupling. Take a look at chapter "Complications with NOESY" in the book "High-Resolution NMR Techniques in Organic Chemistry" by Tim Claridge.
In lactic acid there is no room for chemical exchange aside from hopping of hydroxyl protons to/from water.water, which probably happens too fast for NMR to capture.
Also, the sign of NOE peak depends on the rate of tumbling of the molecule, which depends on the size of the molecule, viscosity of the solvent and temperature. In small molecules that tumble fast NOE peaks will have sign opposite to the diagonal. In larger molecules NOE's will have the same sign. This is because there are two "components" responsible for the emergence of the NOE peaks that make contributions of opposing signs (called zero and double quantum cross-relaxation). Sign of the peak will depend on which component is more significant. Take a look in some NMR text.