/l'ənən/ might be heard in New Zealand.
I'd transcribe the most common pronunciation as /lɪnən/ (as Merriam-Webster does), while Oxford Dict. prefers /lɪnɪn/
PS: You'll notice that the British transcribe words like 'wicked' as /ˈwɪkɪd/, while elsewhere you'll find /wɪkəd/. This is most noticeable in the past tense verbs such as bedded, wedded, batted, pitted, etc.