One root, two faces of the same idea: things that sleep and things that have grown old. The link is intuitive once you see it: what sleeps is dormant, and what stays dormant ages. From לִישֹׁן (to sleep) Hebrew grows יָשָׁן (old), נוֹשָׁן (obsolete), and even לְהִתְיַשֵּׁן (to expire, to lapse). None of these are memorized separately. They are the same three letters seen from different angles. Every word here is verified against pealim, niqqud included.
The same root runs through the verb system. Each binyan is a voice: it bends the one idea into active, passive, causative or reciprocal. Tap to hear.
Only two binyanim are lexicalized here. The pa'al carries the plain physical act (to sleep); the hitpa'el carries the gradual, reflexive process of becoming old, which is exactly why a coupon or a law that lapses uses לְהִתְיַשֵּׁן. The pi'el, hif'il and passive moulds stay empty for this root: that is normal, not every root fills all seven.
Same root letters, different noun moulds (mishkalim). The mould tells you the function: who does it, the act of doing it, or the thing produced.
Strip the prefixes, suffixes and vowels. Three consonants remain, and the meaning lives there.