rush, used for tatami covers, surname
藺 centers on a type of rush plant used for weaving tatami covers; the surname sense is a derived use of the plant name.
藺 combines the plant radical 艹 with 閵, which likely contributes the sound. The character refers to a specific rush plant.
Under the grass top 艹, the gate 門 with a bird 隹 inside suggests a rush plant growing near a gate where birds perch, used for weaving tatami covers.
For リン, imagine a length of rush being woven into a tatami cover, and think of the English word 'linen' (リン) to remember the reading.
softstem bulrush (Scirpus tabernaemontani)
soft rush (Juncus effusus var. decipiens); common rush
Machaerina rubiginosa (species of tropical sedge)
Shichito matgrass (Cyperus malaccensis)
needle spikerush (Eleocharis acicularis)
type of traditional Japanese conical hat
Scirpus hotarui (species of bulrush)