بِعْ is a direct second-person command. لِيَبِعْ addresses a third-person action and therefore uses lām al-amr. لِأَبِعْ and لِنَبِعْ express first-person proposal or volition.
Word / formMeaning / explanation
بِعْ هذا الكتابَsell this book!
لِيَبِعْ هذا الكتابَlet him sell this book.
لِنَبِعْ هذا الكتابَlet us sell this book.
These sentences show how the lām-based request differs from the direct short imperative.