Explanation:

Understanding the sentence:
The sentence states that the speaker lost a key. This key was given to the speaker by someone else in the past.

Verb tense:
The correct verb tense to use in this sentence is the past perfect tense, which is formed by using "had" + past participle. The past perfect tense is used to indicate an action that happened before another action in the past. In this case, the action of losing the key happened after the action of giving the key.

Use of "had given":
In the sentence, the action of giving the key happened before the action of losing the key. Therefore, we use the past perfect tense to indicate this sequence of events. "Had given" is the past perfect tense of the verb "give."

Example:
To further illustrate the use of "had given," consider the following example:
- I lost the key that he had given to me.
In this example, the speaker first received the key from someone else ("he gave me the key"), and then later lost the key.

Alternative verb tenses:
If we were to use a different verb tense in the sentence, it would change the meaning or sequence of events. For example:
- I lost the key that he gave to me.
This sentence suggests that the action of losing the key and the action of giving the key happened at the same time or very close together. The past simple tense ("gave") does not indicate that the giving of the key happened before the losing of the key.

In summary:
The correct answer is "had given" because it accurately reflects the sequence of events in the sentence. The action of giving the key happened before the action of losing the key, which is why we use the past perfect tense.