strive, encourage
勵 centers on pushing oneself or others to make an effort: striving hard and encouraging someone to keep going.
勵 combines 力 (strength, effort) with 厲, which likely contributes the sound and carries a sense of harshness or urging. Together they suggest pushing forward with effort.
The right side 力 is strength, and the left side 厲 looks like a person under a cliff (厂) with a field (田) and a creature (禸) — imagine someone urging a stubborn animal to work the field, striving and encouraging with all their might.
For レイ, picture a coach shouting 'lay it all out!' to encourage the team: lay -> レイ, and the team strives harder.