💡 Detailed Explanation
The correct choice is Option 2: 'Um, won't you lend me a pen?' To ask a close friend for a small favor, the informal request pattern '〜てくれない？' (won't you do...?) is used. '貸してくれない？' matches lending a pen to the speaker. Option 1 ('貸してあげようか？' - Shall I lend it to you?) is offering to lend, which is the opposite of the speaker's need. Option 3 ('借りてほしい' - I want you to borrow) means the speaker wants the friend to borrow something, which is incorrect.