IMO, you really need to have your "lily" identified. Some lily-type plants are much more difficult to control than others (such as Brasinia spp/water shield) .
Several different herbicides are generally effective on lilies, but my favorite is imazapyr. It tends to provide better root-control for emergent plants that grow in deeper water. However, the drawback with topically applied herbicides for lilies is this; for every lily-pad that can be contacted by a surface-application, there are probably 2X+ that still have their pads beneath the surface - which won't be contacted or controlled with a topical/surface application. So, be prepared for repetitive treatments in that scenario.
As mentioned above, when conducting topical applications, a good surfactant is critical for leaf-cuticle penetration. "Burning" through the waxy leaf-surface isn't exactly the metaphor that I'd use, since anything that quickly damages leaf-tissue will actually impede the plant's uptake and translocation of the herbicide. Although Cide-Kick is possibly a decent choice for contact/non-systemic herbicides, a good methylated seed-oil surfactant performs best with imazapyr and glyphosate-based herbicides.
