The lín reading is 'to pour or drench': 淋雨 (to get caught in the rain), 淋浴 (to take a shower). A separate reading lìn appears in medical terms, most notably 淋病 (gonorrhea).
Three-drop water radical on the left, the side-stacking form of 水. Marks the character as a liquid-pouring action: drenching, drizzling, pouring water down. Family of pour-related verbs: 浇 (sprinkle), 泼 (splash), 滴 (drip), 洒 (scatter).
Right 林 (two trees = grove) supplies the sound lín exactly. The image is also evocative: water raining down through a forest canopy, drops falling steadily, a useful mnemonic for 'drench, drizzle'. Same phonetic family: 琳 (fine jade), 临 (approach), 霖 (downpour).