MP3 in its standard use is an a lossy audio compression format. It uses human auditory models to degrades data which the human ear is not (totally) sensitive too. Some sounds actually present in the audio file will not be heard because they are below the threshold of hearing, or they are masked by other sounds, nearby in time or frequency. This information that can be discarded is used to reduce the necessary size in bits to store the audio content.
So, information is lost, and a direct conversion to another audio format, whether lossless or not, will only cause minor changes (because of floating points operations on data and rounding, etc.). Unless in extreme cases (very high compression, very quiet sounds), those are unlikely to be heard.
However, compression standard tell how to decode compressed file streams, and do not disallow postprocessing that can improve the objective or subjective quality of the compressed file. For instance, an image renderer can process a decoded JPEG image to smooth out some border/checkerboard artifacts. The same may occur in audio, eg DSP-based audio post processing enhances audio quality. Based on some models, some processing might be able to compensate for what was lost in the initial MP3 coding.
Last: when original audio data contains noise, surprisingly, compression can enhance the quality, as noise can be discarded first while compressing. This is described in the influential paper (at least to me) Filtering Random Noise from Deterministic Signals via Data Compression by Natarajan in 1995.
So, it is not impossible that converting a lossy format into another lossy format may actually improve quality.