An effective boycott does not raise the price of lettuce. The opposite is what would be conducive to a wage increase.
Agreed. A totally effective boycott results in zero income for everyone involved. A partially effective boycott results in an increase of supply which (usually) results in a reduction in price especially for goods like lettuce which have a short self life.
Honestly I don’t have a ready answer for how to address the cost of labor other than to say it’s also a question of supply and demand. I was watching a documentary about laborers in central/south America who grow cocoa leaves. They make next to nothing, relatively speaking in gringo money. Add some alcohol or ammonia, press it in a hand-press, and move it on up the distribution chain. But the end product gets $10,000+ a pound in the USA.