come, due, next, cause, become
來 centers on movement toward a reference point: coming, arriving, or approaching. Its extended senses of 'next', 'due', 'cause', and 'become' all grow from the idea of something drawing near or resulting from prior movement.
來 is an ancient pictograph of a wheat plant, later borrowed phonetically to mean 'come'. The modern form retains the plant-like shape, but the original meaning is unrelated to its current use.
The shape of 來 resembles a central stalk with drooping leaves or grain heads. Imagine wheat being harvested and brought in—it comes to you, just as the kanji now means 'come'.
For ライ, picture a line of wheat being brought in: line -> ライ, and the wheat comes to the barn.