The correct passive form of the given sentence is:

☀ The lock needs to be oiled.

Let's break down the options:

1. The lock needs being oiled. (Incorrect) This option uses the gerund "being oiled," but it is not the correct passive form. The correct form should use "needs to be oiled."

2. The lock needed being oiled. (Incorrect) This option uses the past tense "needed," which does not match the present tense of the original sentence ("needs"). The correct passive form should use "needs to be oiled."

3. The lock needs to be oiled. (Correct) This sentence correctly uses the passive voice and conveys the same meaning as the original sentence. It uses the correct form "needs to be oiled."

4. The lock need be oiled. (Incorrect) This option omits the word "to," which is necessary in the passive construction. The correct form should use "needs to be oiled," as shown in option 3.