Do I own the file converted to lossless?

I have purchased a lot of music from Apple going back to the iTunes days. This is all in 256 AAC format. If I select these files from Apple’s current catalogue with the hope it will play the higher res lossless version, Apple Music will still play the lower res file that is in the MacBooks local library. Apple Music provides an easy way to convert the local file to lossless. In this case, a second file becomes available in the local library. If I delete the AAC format of the file, the one I purchased, do I own the lossless version? I don’t want to have duplicate versions of the song on my local hard drive, but I also don’t want to delete files I have paid for.