Are my earnings lawful or unlawful, knowing that I work as a voice-over artist and my voice is mixed with music only in the background, and I cannot dictate how my voice is used?

The permissibility of profit or wages is tied to theibility of the work itself. If voiceover work is permissible, then the earnings from it are permissible, regardless of the presence of background music. However, the person who creates the background music is not permitted to earn wages from it. If the questioner knows beforehand that his voiceover will be accompanied by music, it is better for him to seek other work that does not involve music.