What songs is Lucio playing?
Solution 1:
The songs are from Lúcio's (No longer fictional) album, Synaesthesia Auditiva.
The "healing" song is "Rejuvenescência". The "movement speed" song is "We Move Together As One".
Solution 2:
No, Lúcio's ability songs are not in the official soundtrack, but you can download them on Blizzard's Overwatch press page.
Scroll down until you see two WAV files. Those are what you're looking for. You might want to convert them to something more handy, like FLAC, though.