Technically you can have a format which is literally defined in such a way that not all inputs can be perfectly represented. On example is mobile phone audio, i

Technically you can have a format which is literally defined in such a way that not all inputs can be perfectly represented. On example is mobile phone audio, it is defined to operate at a particular bit rate, which is less than that required to represent all possible speech signals. However, you are right that 'lossy' is usually used to describe its intended use rather than its actual formal limit. For example, you can (probably!) non-lossily encode an image as a jpeg, but it won't be as good a compression ratio as you would get from a format which was specifically designed for use with lossless compression. It might even cause the file to get bigger.