come, due, next, cause, become
来 centers on movement toward a point: coming, arriving, or the next thing approaching. The senses of causing or becoming something grow from the idea of bringing about a new state.
to be able to do; to be possible; to be permitted (to do)
to come (spatially or temporally); to approach; to arrive
occurrence; happening; taking place
workmanship; craftsmanship; execution; finish
(distant) future
since; henceforth
originally; primarily
future; (future) prospects
next year
occurrence; happening; incident; event
up to now; so far
next week
origin; source; history; derivation
as much as one can; as much as possible; if at all possible
coming to a store (restaurant, bar, shop, etc.)
to come along; to come around; to turn up
coming to Japan; visit to Japan; arrival in Japan
next month
foreign; imported
arrival; coming; advent
completion; finish
from ancient times; from old times; from time immemorial
coming and going; keeping in touch; visiting each other
pre-existing; already there; conventional
来 originally depicted a wheat plant, and it was borrowed early on for the similar-sounding word meaning 'to come'. The modern form retains the plant-like shape.
Picture a wheat stalk bending toward you as if it is coming closer. The top stroke is like a grain-heavy head nodding forward.
For ライ, imagine a line of wheat plants coming toward you: line -> ライ, and the wheat comes.