Yes, JPG to JPEG XL and back is lossless, but the reverse is nowhere mentioned.

Trying around with some jpg and jxl files I cannot convert jxl losslessly to jpg files even if they are only 8bit. The jxl files transcoded from jpg files show "JPEG bitstream reconstruction data available" with jxlinfo, so I think some extra metadata is stored when going from jpg to jxl to make the lossless transcoding possible. I can imagine not supporting the reverse (which is pretty useless anyway) allowed for more optimizations.