As more line is released into the water, the total line lift force increases. At some point line lift equals the weight and diving forces of the lure. In the special case in which the rod tip is at the surface, any additional line released will stay at the surface, and the line and lure will not go deeper.

In the case in which the rod tip is elevated, the rod lifts the line too, and as more line is released, the longer submerged line provides more lift, and the rod provides less lift (and more horizontal pull) because the line angle  becomes more acute. More line will be suspended and unsubmerged, but the line approaches horizontal at the surface with very little more depth.

At any rate, the lure will not go any deeper than allowed by the balance of lift versus weight and diving force.

For a sinking rig, depth can always be increased by reducing speed, but a floating/diving lure is not affected as much by speed.