No, you don't need a publisher to monetise lyrics, but the process differs for published and independent songwriters. Publishers typically handle lyrics licensing as part of their broader rights management, meaning lyrics revenue flows through them according to your publishing deal terms.
Independent songwriters can work directly with lyrics aggregators or use platform tools to distribute their lyrics. However, you'll need to handle all administration yourself - from ensuring accuracy to managing any disputes. Some aggregators offer different service levels, from basic distribution to full administration.
The trade-off is between control and convenience. Publishers provide infrastructure and expertise but take a share of revenue. Going independent means keeping more revenue but handling more complexity yourself.