
verliehen
awarded
Describes something that was officially given to someone as an honor, prize, or title.
Der ihm verliehene Nobelpreis würdigt seine lebenslange Forschungsarbeit.
The Nobel Prize awarded to him honors his lifelong research work.
awarded / lent
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awarded
Describes something that was officially given to someone as an honor, prize, or title.
Der ihm verliehene Nobelpreis würdigt seine lebenslange Forschungsarbeit.
The Nobel Prize awarded to him honors his lifelong research work.

lent
Describes an object that was given to someone to use for a limited time.
Das verliehene Werkzeug muss bis zum Abend zurückgebracht werden.
The lent tool must be returned by evening.
'Verliehen' is the past participle of the verb 'verleihen' (to award / to lend). It is very often used like an adjective before a noun to describe it.
Der ihm verliehene Orden ist eine große Ehre.
The medal awarded to him is a great honor.
The meaning of 'verliehen' (awarded / lent) depends on the context. If it is about prizes, titles, or medals, it means 'awarded.' If it is about everyday objects like books or tools, it means 'lent.'
Der verliehene Filmpreis war der Höhepunkt des Abends.
The film prize awarded was the highlight of the evening.
In the meaning 'awarded,' 'verliehen' is often used with nouns that express an honor or recognition. Typical examples are: der verliehene Preis (the awarded prize), der verliehene Titel (the awarded title), or die verliehene Medaille (the awarded medal).
Die ihr verliehene Auszeichnung würdigt ihr soziales Engagement.
The award given to her honors her social commitment.
In the meaning 'lent,' 'verliehen' is combined with everyday objects. Common examples are: das verliehene Buch (the lent book), das verliehene Auto (the lent car), or das verliehene Spiel (the lent game).
Ich muss das verliehene Buch heute in die Bibliothek zurückbringen.
I have to return the lent book to the library today.
to assign / to forgive / to miss
When talking about an official honor, both words initially seem appropriate. „Vergeben“ describes allocation in general, while „verliehen“ is especially common for prizes, titles, and honors. „Vergeben“ is usually suitable for a contract or task, while „verliehen“ is typically used for a title or prize.

Die Stadt hat der engagierten Helferin den Ehrenpreis verliehen.
The city presented the dedicated volunteer with the honorary prize.
Die Stadt hat den Auftrag für die neue Brücke an eine Firma vergeben.
The city awarded the contract for the new bridge to a company.