There are various forms of BMP, some with lossless run-length encoding, none with lossy image compression like JPEG. Taking a 24-bit image and putting it in a 24-bit BMP will not be lossy. Any alpha channel from a 32-bit image may be lost because only recent variants of BMP support it. Also if Qt (or Paint) produces a 16-bit or colour mapped BMP then it will be lossy with respect to the original image. It seems the Qt output code will do the right default thing from a cursory inspection of the source (src/gui/image/qbmphandler.cpp).
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