This is not necessarily a Catholic answer, but it's the only answer I can provide. The answer, then, is that it is not clearly demonstrable from Scripture (or any popular tradition) that Satan / Lucifer was the angel of music before his fall. Nonetheless, the reason that some people come to this conclusion is likely based upon taking the following passage and applying it to Satan.
Ezekiel 28:13 KJV
Thou hast been in Eden the garden of God; every precious stone was thy
covering, the sardius, topaz, and the diamond, the beryl, the onyx,
and the jasper, the sapphire, the emerald, and the carbuncle, and
gold: the workmanship of thy tabrets and of thy pipes was prepared in
thee in the day that thou wast created.
There we can see that if this passage, which is typically titled "A Lament over the King of Tyre," if taken as referring Satan metaphorically, can give one reason to think that Satan was the leader of music in heaven. There are more than a few liberal interpretive leaps needed to arrive at such a conclusion; nonetheless, this would be the only passage I can find that would fit such a theory.
Pulpit commentary offers this:
The workmanship of thy tabret and pipes; better, the service. The Authorized Version and Revised Version follow Luther. Keil agrees as to "tabret" (so Genesis 31:27; Isaiah 5:12; elsewhere, as in Exodus 15:20 and Job 21:12, the Authorized Version gives "timbrels"), but takes the latter word (not found elsewhere) as identical with its feminine form, and meaning "female." He sees in the clause, accordingly, a picture of the pomp of the Tyrian king, surrounded by the odalisques of the harem, who, with their timbrels, danced to his honor as their lord and king (camp. Isaiah 23:16; Exodus 15:20; 1 Samuel 18:6).