Do you lose quality converting from a lossy audio format to a lossless format?

"Nope.

When you convert from FLAC to MP3 (or whatever formats), the converter has to essentially re-record the file. It would be like taking a video of a video, or taking a photo of a photo; of course you're not going to maintain the quality of the original.

However, when you convert from MP3 to FLAC, you're simply decompressing the MP3 and taking the raw sound of whatever is there. No quality loss. Of course, as James Polley pointed out in the comments, you can't gain quality out of nothing in this way.

This applies to audio, video, images, etc."