Here are some statements which you can compile into the answer of the question which you have but we do not know about:
- downsizing cannot be lossless period
- downsizing by 1/2, 1/3, 1/4 etc means that no resampling is required and will preserve image apperance somewhat better
- however, most images (particularly unedited images from cameras with Bayer sensors) do not require the resolution which they have for preserving details which they have, i.e. have surplus information some of which may be wasted without visual effect, and resampling will not be too bad in this case
- image encoding is abstracted from any visible manipulation in vast majority of cases. Image encoding is most oftenly (have not seen a counter example yet) preserving image pixel dimensions, therefore there is no sense in asking about how resizing is related to lossless
- image encoding may affect following characteristics directly or indirectly: bit depth, tone distribution, chromatic resolution
- image encoding may create artifacts (false details) of different kinds (for example, low quality JPEG2000 is quite different from LQ JPEG)
- resizing can be done with various algorythms from which the worst one is "nearest neightbour", the better one is "bilinear", the one which is fine in all cases is "bicubic", the one which is good for resizing unsharped picture is "bicubic sharper" (increases sharpness along with downsizing, should be applied carefully to sharpened images), and probably the best of all available is "Lanczos" (does not include sharpening).
- there are numerous image encoding algorythms from which I recommend to try JPEG2000, WebP and FLIF (may be lossless and lossy) or, if you do not have particular interest in quality, you will be fine with JPEG. PNG encoding is good for images with big uniform areas which do not contain noise (this is important).
- PNG encoding can be lossy depending on implementation but when there are no options in software to choose lossy/lossless (most of the software does not), it is safe to assume that image will be compressed losslessly.
P.S. I am intentionally saying that there may be no resampling in case of said resizing scale because for resampling to occur there should be an interpolant first but it is not required to compute an interpolant if all input pixels are strictly divided between output pixels and cannot influence other pixels. It is of course possible to implement resizing in such a way that interpolant is always computed but it still is NOT required (this is what I said originally, not that resampling is always skipped in this case).
It might be proven that if continious image is sampled with
(N*A)x(N*B) samples then latter may be exactly reduced to former without ANY signal loss. This is what provides somewhat better quality, not the absence of resampling itself.
It is common to name any change in discretisation "resampling" but I ignore that (in same way as I ignore the commond statement saying that long focal length objectives compress perspective). Please create a chat if you want to disprove my statements.
P.P.S. The Nyquist-Shannon theorem is related to this, BTW.