languid, be lazy, be negligent
懶 centers on a lack of energy or will to act: being languid, lazy, or negligent in one's duties.
懶 combines 忄 (heart/mind) with 賴, which likely contributes the sound and carries a sense of relying or leaning, suggesting a mind that leans toward inaction.
The heart radical 忄 beside 賴 (which can suggest dependence) paints a picture of a heart that just wants to lean back and do nothing—pure laziness.
For ラン, imagine a lazy person lounging on a rancho (a made-up lazy ranch), too languid to get up: ran -> ラン.