Border I'm filling in (5)

I believe the answer is:

limit

I'm a little stuck... Click here to teach me more about this clue!

'border' is the definition.
(I've seen this in another clue)

'i'm filling in' is the wordplay.
'filling' becomes 'lit' (I can't justify this - if you can you should believe this answer much more).
'in' indicates putting letters inside.
'im' going within 'lit' is 'LIMIT'.

Can you help me to learn more?

(Other definitions for limit that I've seen before include "Confine within bounds" , "Curb" , "Utmost" , "Ration" , "Outer extent" .)

I've seen this clue in The Times.

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