Lossless compression is not about importance of data. Lossless is lossless, if the result of a roundtrip is not EXACTLY IDENTICAL then it is by definition not lossless but lossy.
Maybe you're confusing with "visually lossless" compression, which is a rather confusing euphemism for "lossy at sufficiently high quality".
JPEG XL can do both lossless and lossy. Lossless JPEG XL, like any other lossless image format, stores sample values exactly without losing anything. That is why it is called "lossless" — there is no loss whatsoever.
Maybe you're confusing with "visually lossless" compression, which is a rather confusing euphemism for "lossy at sufficiently high quality".
JPEG XL can do both lossless and lossy. Lossless JPEG XL, like any other lossless image format, stores sample values exactly without losing anything. That is why it is called "lossless" — there is no loss whatsoever.