If those peaks are correlations between J-coupled protons, then such shape is likely caused by the coupling, but data truncation as Dan mentioned can explain such pattern too.

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, 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 (so in lactic acid NOE peaks are negative). In larger molecules NOE's will have the same sign as the diagonal peaks. 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.

Hi Dmitry, we can't really help without an image - but what your describing sounds a lot like truncation artifacts:

Certain NOESY signals can be very strong, and without appropriate windowing can take a 'sinc-wriggle' shape. This is often corrected for by using an exponential windowing function or similar before the Fourier transform.

Looks like sinc wiggles in both dimensions due to truncation of the data which may be caused by having a strong signal. This could be fixed when processing the data by introducing window functions that make the signal decay to zero (artificially) before the end of collection of the data. Hard to tell without a real figure to go off.