Final answer:
In the sentence 'The students accompanied by their lecture are planning a tour', the correct verb to use is 'are' because the subject 'The students accompanied by their lecture' is plural.
Step-by-step explanation:
The subject of the sentence in question "The students accompanied by their lecture are/is planning a tour" is 'The students accompanied by their lecture.' This subject is plural because it refers to more than one student, and the lecturer is included as part of the accompanying group, not as an additional subject. We therefore use the plural form of the verb, which is 'are.'