Just by itself, the DWT is lossless, because you can simply invert the transform. However, if you are really going to compress the image, then you are by definition modifying the coefficients and you have lossy compression.
For example:
x = magic(4);
[ca,ch,cv,cd] = dwt2(x,'db1','mode','sym');
X = idwt2(ca,ch,cv,cd,'db1','mode','sym');
max(abs(X-x))
In practice, the above is not useful. So you would modify the coeffcients in a way that you would not be able to get back the original image exactly -- hence lossy.
